Question

What is the value of (cos square 67-sin square 23)?

Answer 1

Hey there!

We know that,
cos²B - sin²A = cos(A + B) * cos ( A - B)

Now,
cos²67° - sin²23°
= cos(67 + 23 ) * cos( 67 - 23 )
= cos ( 90 ) * cos45
= 0 * 1/√2 .
= 0

$\therefore$ cos²67 -sin²23 = 0 .

Quick Alternative : [ cos²67-sin²23 = cos²(90-23) - sin²23 = sin²23 - sin²23 = 0 ]

[ cos²67-sin²23 = cos²67-sin²(90-67) = cos²67-cos²67 = 0 ]

Hope helped!

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