Question

2sin67 (1/2)⁰ cos22(1/2)⁰=_______
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Answer 1

Answer:

(√2+1)/√2

Step-by-step explanation:

2sin67 (1/2)⁰ cos22(1/2)⁰

= 2 sin (90 - 22(1/2) )⁰ . cos22(1/2)⁰

= 2.cos22(1/2)⁰.cos22(1/2)⁰

= 2cos²22(1/2)⁰

[ we know cos2A = 2cos²A - 1

=> 2 cos²A = 1+cos2A ]

so, 2cos²22(1/2)⁰ = 1+cos45°

                             = 1+ (1/√2)

                             = (√2+1)/√2