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Trigonometry Practice Test 1

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Question : 3 of 40

Marks: +1, -0

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

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

?

2
$2^2$
$2^3$
1
None of these

Solution: 👈: Video Solution

Concept:

The equation fixes the value of

\sin\theta

, which can then be used to evaluate

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

.

Explanation:

\sin\theta+\csc\theta=2

\Rightarrow \sin\theta+\frac{1}{\sin\theta}=2

\Rightarrow \sin^2\theta-2\sin\theta+1=0

\Rightarrow (\sin\theta-1)^2=0

\Rightarrow \sin\theta=1

So,

\theta=90^\circ

.

Now,

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

=\sin^4 90^\circ+\cos^4 90^\circ

=1^4+0^4

=1

Answer:

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

, so option D is correct.

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