Question
What is the simplified value of the given
expression? 4(sin² 20° + sin² 70°) + 2sin 30° - (2sec 60° + cot 45°)Solution
4(sin ² 20° + sin ² 70°) + 2sin 30° - (2sec 60° + cot 45°)
Using, sin(90° - A) = cos A
= 4{sin ² 20° + sin ² (90 - 20)°} + 2 x 1/2 - {2 x 2 + 1}
= 4(sin ² 20° + cos ² 20°) + 1 – 5
Using, sin ² A + cos ² A = 1
= 4 x 1 + 1 - 5 = 4 + 1 - 5 = 0
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