Question Bank - Mathematics

Here's the question bank on all the mathematics topics.

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If 3 sin-1x + cos-1x = ?, then what is x equal to?

A.
0
B.
\(\frac{1}{2}\)
C.
\(\frac{1}{\sqrt 2}\)
D.
\(\frac{1}{\sqrt 3}\)

Solution:

Concept :sin-1 x + cos-1 x = ?/2, x ? [-1, 1]Calculation:Given: 3 sin-1 x + cos-1 x = ? ? 3 sin-1 x + cos-1 x = 2 sin-1 x + [sin-1 x + cos-1 x] = ? As we know that, sin-1 x + cos-1 x =\(\frac{\pi}{2}\), x ? [-1, 1]? 2 sin-1 x + [\(\frac{\pi}{2}\)] = ?? 2 sin-1 x = ? - \(\frac{\pi}{2}\)? 2 sin-1 x = \(\frac{\pi}{2}\)? sin-1 x = \(\frac{\pi}{4}\)? x = sin \(\frac{\pi}{4}\) = \(\frac{1}{\sqrt2}\)

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