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
secx2=6−2
d
tanx2=(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 tanx=sin20∘2cos40∘−cos20∘=sin20∘cos40∘+cos40∘−cos20∘=sin20∘cos40∘+2sin30∘sin−10∘=sin20∘sin50∘−sin10∘=sin20∘2cos30∘sin20∘=13 or x=30∘