If (90^{} - θ) + θ = {2} (90^{} - θ), then the value of cosec θ is

Correct Answer is : 3/2{3/2}3/2

Correct Answer is : 3/2{3/2}3/2

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SSC CHSL 20 Dec 2015 Shift 1 Paper

Question : 101 of 200

Marks: +1, -0

\sin(90^{\circ} - \theta) + \cos \theta = \sqrt{2} \cos(90^{\circ} - \theta)

, then the value of cosec θ is

Solution:

Given,

\sin(90^{\circ} - \theta) + \cos \theta = \sqrt{2} \cos(90^{\circ} - \theta)

........(1)

We know that,

\sin(90^{\circ} - \theta) \cos \theta

and

\cos(90^{\circ} - \theta) \sin \theta

Now, Equation (1) can be written as,

\cos \theta + \cos \theta = \sqrt{2} \sin \theta

(or)

2 \cos \theta = \sqrt{2} \sin \theta

Squaring on bothsides we get,

2 \cos^2 \theta = \sin^2 \theta

⇒

2(1 - \sin^2 \theta) \Rightarrow \sin^2 \theta

\Rightarrow 2 - 2\sin^2 \theta = \sin \theta

\Rightarrow 2 = 3\sin^2 \theta

\Rightarrow 2 = 3\left( \frac{1}{\csc^2 \theta} \right) \Rightarrow \csc^2 \theta = \frac{3}{2}

⇒ cosecθ =

\sqrt{3/2}

Hence, option B is the correct answer.

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