Question

The value of $\frac{cos(90^{0}-\Theta)sec(90^{0}-\Theta)tan\Theta}{cosec(90^{0}-\Theta)sin(90^{0}-\Theta)cot(90^{0}-\Theta)}+\frac{tan(90^{0}-\Theta)}{cot\Theta}$ is
(a)1
(b)− 1
(c)2
(d)−2

Answer 1

SOLUTION :  

The correct option is (c) : 2 .

Given :  [cos (90° - θ) sec (90° - θ) tan θ / cosec (90° - θ) sin (90° - θ) cot (90° - θ)] + tan (90° - θ)/cot θ

= [ (sin θ cosec θ tan θ) / (sec θ cos θ tan θ) ] + cot θ/cot θ

= [1 × tan θ / 1 × tan θ]  + 1

[ sin θ × cosec θ = 1, sec θ cos θ = 1]

= [ tan θ / tan θ] + 1

= 1 + 1  

= 2  

Hence, the value of   [cos (90° - θ) sec (90° - θ) tan θ / cosec (90° - θ) sin (90° - θ) cot (90° - θ)] + tan (90° - θ)/cot θ is 2 .

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Answer 2

option (c) is correct