Question

cos^2 pi/8 + 4cos^2 pi/4 - sec pi/3 + 5tan^2 pi/3 + sin^2 pi/8

Answer 1

Given : cos^2 pi/8 + 4cos^2 pi/4 - sec pi/3 + 5tan^2 pi/3 + sin^2 pi/8

To Find : Value

Solution:

cos² π/8 + 4cos² π/4 - sec π/3 + 5tan² π/3 + sin² π/8

= cos² π/8 + sin² π/8 + 4cos² π/4 - sec π/3 + 5tan² π/3

cos² π/8 + sin² π/8 = 1

= 1  + 4cos² π/4 - sec π/3 + 5tan² π/3

cos² π/4 = (1/√2)²  = 1/2

sec π/3 = 2

tan² π/3  = (√3)²  = 3

= 1 + 4(1/2) - 2  + 5(3)

= 1 + 2 - 2 + 15

= 16

cos² π/8 + 4cos² π/4 - sec π/3 + 5tan² π/3 + sin² π/8 = 16

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