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Q.

If sin(x + 20°) - 2 sin x cos 40°, where x∈(0,π/2), then which of the following hold(s) good?

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a

cos 2x: 1/2

b

cosec 4x = 2

c

sec⁡x2=6−2

d

tan⁡x2=(2−3)

answer is A.

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Detailed Solution

sin x cos20° + cos x sin20° - 2 sin x cos40°or sin20° cos x - sin x(2 cos40° - cos20°)or tan⁡x=sin⁡20∘2cos⁡40∘−cos⁡20∘=sin⁡20∘cos⁡40∘+cos⁡40∘−cos⁡20∘=sin⁡20∘cos⁡40∘+2sin⁡30∘sin⁡−10∘=sin⁡20∘sin⁡50∘−sin⁡10∘=sin⁡20∘2cos⁡30∘sin⁡20∘=13 or x=30∘
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