Statement I- If mcos-ncos- then tan-tan- m-n-m-nStatement II- If sin-sin-a-b-a-b then tan-ab- Which of the above statements is correct-

The correct option is B Only II mcos( θ +α nbsp;) =ncos( θ α nbsp;) ⇒ cos( θ +α nbsp;) nbsp; cos( θ α nbsp;) nbsp; = m n Using compon ...

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Standard XII

Mathematics

Differentiation of Inverse Trigonometric Functions

Statement I: ...

Question

Statement I: If $m cos (θ + α) = n cos (θ - α)$ then $tan θ . tan α = \frac{m + n}{m - n}$
Statement II: If $\frac{sin (α + β)}{sin (α - β)} = \frac{a + b}{a - b}$ then $tan α . cot β = \frac{a}{b}$ .
Which of the above statements is correct?

Only I

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Only II

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Both I and II

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Neither I nor II

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Solution

The correct option is B Only II
$m c o s (θ + α) = n c o s (θ - α) \Rightarrow \frac{c o s (θ + α)}{c o s (θ - α)} = \frac{m}{n}$
Using componendo and dividendo, we get
$\Rightarrow \frac{c o s (θ + α) + c o s (θ - α)}{c o s (θ + α) - c o s (θ - α)} = \frac{m + n}{m - n} \Rightarrow \frac{2 c o s θ c o s α}{- 2 s i n θ s i n α} = \frac{m + n}{m - n} \Rightarrow c o t θ c o t α = \frac{n + m}{n - m} \Rightarrow t a n θ t a n α = \frac{n - m}{n + m}$
Hence statement I is wrong
$\frac{s i n (α + β)}{s i n (α - β)} = \frac{a + b}{a - b}$
Using componendo and dividendo, we get
$\Rightarrow \frac{s i n (α + β) + s i n (α - β)}{s i n (α + β) - s i n (α - β)} = \frac{a}{b} \Rightarrow \frac{2 s i n α c o s β}{2 c o s α s i n β} = \frac{a}{b} \Rightarrow t a n α c o t β = \frac{a}{b}$
Hence statement II is true

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Similar questions

Q. Statement (I): If

sin α = \frac{12}{13}, (0 < α < \frac{π}{2})

and

cos β = - \frac{3}{5}, (π < β < \frac{3 π}{2})

then

sin (α + β) = \frac{56}{65}

Statement (II): If

θ

and

ϕ

are angles in the first quardrant such that

tan θ = \frac{1}{7}

and

sin ϕ = \frac{1}{\sqrt{10}}

then

θ + 2 ϕ = 45^{0}

Which of the above statements is correct?

Q. Statement I: lf

α, β

are the roots of

x^{2} - a x + b = 0

, then the equation whose roots are

\frac{α + β}{α}, \frac{α + β}{β}

b x^{2} - a^{2} x + a^{2} = 0

Statement II: lf

α, β

are the roots of

x^{2} - b x + c = 0

and

α + h, β + h

are the roots of

x^{2} + q x + r = 0

, then

h = b - q

.
Which of the above statement(s) is(are) true.

Q. If

\frac{sin (α + β)}{sin (α - β)} = \frac{a + b}{a - b}

, where

α \neq β, a \neq b, b \neq 0

, then

\frac{tan α}{tan β}

If $c o s (θ - α)$ = a, $s i n (θ - β)$ = b,

then $c o s^{2} (α - β)$ + 2ab $s i n (α - β)$ is equal to

Q. Let A and

B

denote the statements

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B

sin α + sin β + sin γ = 0

cos (β - γ) + cos (γ - α) + cos (α - β) = - 3 / 2

, then

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Statement I: If mcos(θ+α)=ncos(θ−α) then tanθ.tanα=m+nm−nStatement II: If sin(α+β)sin(α−β)=a+ba−b then tanα.cotβ=ab. Which of the above statements is correct?

Statement I: If $m cos (θ + α) = n cos (θ - α)$ then $tan θ . tan α = \frac{m + n}{m - n}$
Statement II: If $\frac{sin (α + β)}{sin (α - β)} = \frac{a + b}{a - b}$ then $tan α . cot β = \frac{a}{b}$ .
Which of the above statements is correct?