Question

find 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

The given question is wrong.

However,

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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