What is the value of cossquare 67 - sinsquare 23 degree
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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....
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....
Answered by
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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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