Question

What is the value of
( cos²67°-sin²23°)

Answer 1

Convert cos^67 to sin or convert sin^23 to cos and we'll get the value of expression 1.

Answer 2

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!