1.

Find the value of the expression: cos2(π/8) + 4cos2(π/4) – sec2(π/4) + 2tan2(π/3) + sin2(π/8)1. 52. 73. 94. 11

Answer» Correct Answer - Option 2 : 7

 

Given:

cos2(π/8) + 4cos2(π/4) – sec2(π/4) + 2tan2(π/3) + sin2(π/8)

Concept Used:

cos2θ + sin2θ = 1

π = 180° 

Calculation:

cos2(π/8) + 4cos2(π/4) – sec2(π/4) + 2tan2(π/3) + sin2(π/8)

⇒ {cos2(π/8) + sin2(π/8)} + 4cos245° – sec245° + 2tan260°

⇒ 1 + 4(1/√2)2 – (√2)2 + 2(√3)2

⇒ 1 + 2 – 2 + 6

⇒ 7

∴ The value of the expression cos2(π/8) + 4cos2(π/4) – sec2(π/4) + 2tan2(π/3) + sin2(π/8) is 7.



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