Question

Evaluate:
(cos^2 20+cos^2 70/sec^2 50-cot^2 40)+2cosec^2 58-2cot58.​

Answer 1

Answer:

Step-by-step explanation:

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[{2/3 cosec^2 (58)} - {2/3 (cot 58)( tan 32)} - {5/3 (tan 13)( tan 37 )( tan 45 )( tan 53 )( tan 77)}]

Using: tan x = cot (90 - x)

={[2/3 cosec^2 58} -{2/3 cot^2 58} - {5/3 (tan 13 tan 37 tan 45 cot 37 cot 13}]

=2/3(cosec^2 58 - cot^2 58) - 5/3 [since, tan 45 = 1]

=2/3 -5/3 [Using cosec^2 x - cot^2 x = 1]

= -1

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