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Question

Evaluate sin 50°÷cos 40°+cosec40°÷sec50°- 4cos52°.cosec38°

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Solution

sin50/cos 40 +cosec 40/ sec50 -4cos52 cosec 38

cos(90-50)/cos 40 +sec(90-40)/sec 50 -4 cos(90-38) cosec 38 since cos (90-x) =sinx , sec(90-x)=cosecx

cos40/cos40 +sec 50/sec50 -4 cos 50 sec50

1+1-4 since sin x cosec x=1

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