Question

What is the value of cos^267°-sin^223°

Answer 1

Trigonometry is the study of the relationship between the sides and angles of a triangle.
Two angles are said to be complementary,of their sum is equal to 90°. We have following relations between different trigonometric ratios.
sin(90 - A) = cosA
cos(90 - A) = sinA
tan(90 - A) = cotA
cot(90 - A) = tanA
sec(90 - A) = cosecA
cosec(90 - A) = dev
SOLUTION :
GIVEN : cos²67° - sin²23°
cos²(90° - 23°) - sin²23°
sin²23° - sin²23° = 0
[cos(90 - A) = sinA]
Hence, the value of cos²67° - sin²23° is 0 (zero).

HOPE THIS WILL HELP YOU...

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!