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Tangent, Cota...

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Trending Questions

Q.

If $α, β, γ, ẟ$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$ , then the value of $4 \sin \frac{α}{2} + 3 \sin \frac{β}{2} + 2 \sin \frac{γ}{2} + \sin \frac{ẟ}{2}$ is equal to

$2 \sqrt (1 - k)$
$\frac{1}{2} \sqrt (1 + k)$
$2 \sqrt (1 + k)$
None of these

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Q. The numerical value of

(1 + cot x - cosec x) (1 + tan x + sec x)

is

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Q.

How do you find the exact values of $\sin^{- 1} (\frac{1}{2})$ ?

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Q. The value of

sin 75^{\circ} + cos 75^{\circ}

is

$\frac{\sqrt{3}}{\sqrt{2}}$
$\frac{1}{\sqrt{2}}$
$\frac{\sqrt{3} - 1}{\sqrt{2}}$
$\frac{\sqrt{3} + 1}{\sqrt{2}}$

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Q. If

θ \in (0, \frac{π}{4})

and

t_{1} = (tan θ)^{tan θ},

t_{2} = (tan θ)^{cot θ},

t_{3} = (cot θ)^{tan θ}

and

t_{4} = (cot θ)^{cot θ}

then

$t_{1} > t_{2} > t_{3} > t_{4}$
$t_{4} > t_{3} > t_{1} > t_{2}$
$t_{3} > t_{1} > t_{2} > t_{4}$
$t_{2} > t_{3} > t_{1} > t_{2}$

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Q. If

θ \in (0, \frac{π}{4})

and

t_{1} = (tan θ)^{tan θ},

t_{2} = (tan θ)^{cot θ},

t_{3} = (cot θ)^{tan θ}

and

t_{4} = (cot θ)^{cot θ}

then

$t_{1} > t_{2} > t_{3} > t_{4}$
$t_{4} > t_{3} > t_{1} > t_{2}$
$t_{3} > t_{1} > t_{2} > t_{4}$
$t_{2} > t_{3} > t_{1} > t_{2}$

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Q. The value of

sin 75^{\circ} + cos 75^{\circ}

is

$\frac{\sqrt{3}}{\sqrt{2}}$
$\frac{1}{\sqrt{2}}$
$\frac{\sqrt{3} - 1}{\sqrt{2}}$
$\frac{\sqrt{3} + 1}{\sqrt{2}}$

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Q. If

sin (θ + α) = cos (θ + α)

, then which of the following is/are correct?
where

θ, α \in (0, \frac{π}{2}) - {\frac{π}{4}}

$tan α = \frac{1 - tan θ}{1 + tan θ}$
$tan α = \frac{1 + tan θ}{1 - tan θ}$
$tan θ = \frac{1 + tan α}{1 - tan α}$
$tan θ = \frac{1 - tan α}{1 + tan α}$

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Q. If

180^{\circ}

<

θ

<

270^{\circ}

and

sin θ = - \frac{5}{13}

then 5

{cot}^{2} θ + 12 tan θ + 13 c o s e c θ

=

\N
-1
1
2

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Q. If

tan A = \frac{x sin B}{1 - x cos B}

and

tan B = \frac{y sin A}{1 - y cos A}

then

\frac{sin A}{sin B} =

$\frac{x}{y}$
$\frac{y}{x}$
$x + y$
$x - y$

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Q. If

\frac{1 + sin 2 x}{1 - sin 2 x} = {cot}^{2} (a + x)

\forall x \in R - (n π + \frac{π}{4}),

n \in N

then the possible value of

a

is

$\frac{π}{4}$
$\frac{π}{2}$
$\frac{3 π}{4}$
$\frac{3 π}{2}$

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Q. If

sin (θ + α) = cos (θ + α)

, then which of the following is/are correct?
where

θ, α \in (0, \frac{π}{2}) - {\frac{π}{4}}

$tan α = \frac{1 - tan θ}{1 + tan θ}$
$tan α = \frac{1 + tan θ}{1 - tan θ}$
$tan θ = \frac{1 + tan α}{1 - tan α}$
$tan θ = \frac{1 - tan α}{1 + tan α}$

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Q. The numerical value of

(1 - cos x) (1 + cos x) (1 + {cot}^{2} x)

is

$0$
$1$
$2$
$3$

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Q. If

tan A = \frac{x sin B}{1 - x cos B}

and

tan B = \frac{y sin A}{1 - y cos A}

then

\frac{sin A}{sin B} =

$\frac{x}{y}$
$\frac{y}{x}$
$x + y$
$x - y$

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Q. The value of

sin \frac{π}{5} sin \frac{2 π}{5} sin \frac{3 π}{5} sin \frac{4 π}{5}

is

$\frac{5}{16}$
$\frac{11}{16}$
$\frac{13}{16}$
$\frac{3}{16}$

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Q. If

sin A = \frac{12}{13}, cos B = - \frac{3}{5}, 0 < A < \frac{π}{2},

π < B < \frac{3 π}{2}

, then the value of

sin (A + B)

is

$\frac{33}{65}$
$- \frac{1}{63}$
$- \frac{56}{65}$
$- \frac{63}{65}$

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Q. The expression

\frac{tan A}{1 - cot A} + \frac{cot A}{1 - tan A}

can be written as :

$sin A \cdot cos A + 1$
$sec A \cdot cosec A + 1$
$tan A + cot A$
$sec A + cosec A$

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Q. If

sin A + sin B + sin C = 0

and

cos A + cos B + cos C = 0

, then the value of

sin (\frac{A - B}{2})

is

(where A, B, C \in [0, 2 π])

$1$
$\frac{1}{2}$
$\frac{1}{\sqrt{2}}$
$\frac{\sqrt{3}}{2}$

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Q. If

S_{n} = {sin}^{2} \frac{π}{n} + {sin}^{2} \frac{2 π}{n} + \dots + {sin}^{2} \frac{(n - 1) π}{n}

, then the value of

S_{100}

is

$49$
$50$
$\frac{99}{2}$
$\frac{101}{2}$

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