Question

If tan theta=3/4 then find the value of cos2 theta-sin2 theta

Answer 1

tan Ф = perpendicular/base = 3/4
Let perpendicular = 3x and base = 4x
According to pythagoras theorm
Hypotenuse² = perpendicular² + base²
                       = (3x)² + (4x)²
                       = 9x² + 16x²
                       = 25x²
Hypotenuse = √25x² = 5x

Sin Ф = perpendicular/hypotenuse = 3x/5x = 3/5
cos Ф = base/hypotenuse = 4x/5x = 4/5

cos² Ф - sin² Ф = (4/5)² - (3/5)²
                          = 16/25 - 9/25
                          = 7/25

Answer 2

Answer:

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