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Question 129
If $$(sin α + cosec α)^{2} + (cos α + sec α)^{2} = k + tan^{2}α + cot^{2}α,$$ then the value of k is
Solution
Consider , $$(sin α + cosec α)^{2} + (cos α + sec α)^{2}$$
$$sin^{2}α + cosec^{2}α + 2sin α cosec α + cos ^{2}α+ sec^{2}α + 2cos α sec α$$
$$sin^{2}α + (1+cot^{2}α) + 2sin α cosec α + cos ^{2}α+ (1+tan^{2}α) + 2cos α sec α$$
$$(sin^{2}α + cos ^{2}α) + 1+cot^{2}α + 2 + 1+tan^{2}α + 2$$
$$7+ tan^{2}α + cot^{2}α$$
Hence, k = 7
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