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RRB NTPC Mains or Stage 2 Model Paper 5 with solutions

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Question : 19 of 120

Marks: +1, -0

If sin θ+ cosecθ = 2, then what is the value of

\sin^4 \theta + \cos^4 \theta ?

2
$2^2$
$2^3$
1

Solution:

Concept:

Use

\operatorname{cosec}\theta=\frac{1}{\sin\theta}

and solve for

\sin\theta

.

Explanation:

Given:

\sin\theta+\operatorname{cosec}\theta=2

.

Let

\sin\theta=x

.

Then

x+\frac{1}{x}=2

.

So

x^2+1=2x

.

Thus

x^2-2x+1=0

.

Hence

(x-1)^2=0

.

Therefore

x=1

, so

\sin\theta=1

.

Then

\cos^2\theta=1-\sin^2\theta=1-1=0

.

Now

\sin^4\theta+\cos^4\theta=1^4+0^4=1

.

Answer:

The value is

1

, which matches option D.

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