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Question
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
Options
9
7
5
3
Solution
7
Explanation;
(sin α + cos α)2 + (cos α + sec α)2
= sin2α + cosec2α + 2 sin α cosec α + cos2α + sec2α + 2 cos α sec α
= 1 + cosec2α + 2 + sec2α + 2
= 1 + cot2α + 1 + 2 + tan2α + 1 + 2
= 7 + tan2α + cot2α
k = 7
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