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Trigonometry Practice Test 1

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Question : 18 of 40

Marks: +1, -0

If sin x - cos x = 0, then what is the value of

\sin^4 x + \cos^4 x

?

1
$\frac{3}{4}$
$\frac{1}{2}$
$\frac{1}{4}$
None of these

Solution: 👈: Video Solution

Concept:

If

\sin x = \cos x

, then both values have equal magnitude, so

\sin x = \cos x = \frac{1}{\sqrt{2}}

for the standard angle.

Explanation:

Given:

\sin x - \cos x = 0

.

So,

\sin x = \cos x

.

Thus,

\tan x = 1

.

Therefore,

x = \frac{\pi}{4}

.

Now,

\sin^4 x + \cos^4 x = \sin^4 \frac{\pi}{4} + \cos^4 \frac{\pi}{4}

.

Since

\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}

,

\sin^4 x + \cos^4 x = \left(\frac{1}{\sqrt{2}}\right)^4 + \left(\frac{1}{\sqrt{2}}\right)^4

.

= \frac{1}{4} + \frac{1}{4}

.

= \frac{1}{2}

.

Answer:

\frac{1}{2}

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