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Graph of Trigonometric Ratios

if tan theta ...

Question

if tan theta + 4 = 3 ( 4 cot theta +1) where 0° < theta < 90°, then the value of 15/sec theta cosec theta

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s e c θ - c o s e c θ = 0, t h e n t h e v a l u e o f t a n θ + c o t θ

\frac{cosecθ + cotθ}{cosecθ - cotθ} = (cosecθ + cotθ)^{2} = 1 + 2 \cot^{2} + 2 cosecθ cotθ

\frac{secθ + tanθ}{secθ - tanθ} = (secθ + tanθ)^{2} = 1 + 2 \tan^{2} θ + 2 secθ tanθ

θ

is in the first quadrant and

cos θ = \frac{3}{5}

, then value of

5 tan θ - 4 c o s e c θ s e c θ - 4 cot θ

Q. The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is

(a) 1
(b) 2
(c) 4
(d) 0

Q. The value of

\frac{\cos (90 ° - θ) \sec (90 ° - θ) \tan θ}{cosec (90 ° - θ) \sin (90 ° - θ) \cot (90 ° - θ)} + \frac{\tan (90 ° - θ)}{\cot θ}

is

(a) 1
(b) − 1
(c) 2
(d) −2

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