Question

what is the value of cos square 67°- sin square 23°

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

The value of $\cos ^{2} 67-\sin ^{2} 23$ is "1".

Step-by-step explanation:

We have,

$\cos ^{2} 67-\sin ^{2} 23$

To find, the value of $\cos ^{2} 67-\sin ^{2} 23=?$

∴ $\cos ^{2} 67-\sin ^{2} (90-67)$

$=\cos ^{2} 67-\cos ^{2} 67$

[ ∵ $\sin (90-\theta)=\cos \theta$]

$=0$

Hence, the value of $\cos ^{2} 67-\sin ^{2} 23$ is "1".