Question

If sin(50 - 3/2 alpha) = cos(3 alpha - 50),then find the value of alpha and hence evaluate : tan alpha×sec alpha×sin alpha - cot alpha×sin alpha×cos alpha

Answer 1

sin(50°-3/2α)=cos(3α-50°)
or, sin(50°-3/2α)=sin{90°-(3α-50°)}
or, 50°-3/2α=90°-3α+50°
or, -3/2α+3α=90°
or, (-3α+6α)/2=90°
or, 3α=90°×2
or, α=180°/3
or, α=60°
∴, tanαsecαsinα-cotαsinαcosα
=tan60°sec60°sin60°-cot60°sin60°co60°
=√3×2×√3/2-1/√3×√3/2×1/2
=3-1/4
=(12-1)/4
=11/4 Ans.

Answer 2

Answer:

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