Question

cos^2 67°-sin^2 23° ? evaluate

Answer 1

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Here is your answer...

$\cos ^{2} (67 \degree) - \sin^{2} (23 \degree) \\ \\ = \sin^{2} (90 \degree - 67 \degree) - \sin^{2} (23) \\ \\ = \sin^{2} (23\degree) - \sin ^{2} (23\degree) = 0$

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Answer 2

To find:

Cos^2 67 -  Sin^2 23

Solution:

By formula,

Cos^2A - Sin^2B = Cos ( A + B ) * Cos ( A - B )

Here,

A = 67

B = 23  

Substituting,

We get,

Cos (67 + 23 ) * Cos( 67 - 23 )

Cos ( 90 ) * cos ( 45  )

Substituting values,

0 * 1/√2 .

Hence, Cos^2 67 -  Sin^2 23 = 0

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