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Question
Evaluate without using trigonometric tables,
`sin^2 28^@ + sin^2 62^@ + tan^2 38^@ - cot^2 52^@ + 1/4 sec^2 30^@`
Solution
`sin^2 28^@ + sin^2 62^@ + tan^2 38^@ - cot^2 52^@ + 1/4 sec^2 30^@`
= `sin^2 28^@ + sin^2(90^@ - 28^@) + tan^2 38^@ - cot^2 (90^@ - 38^@) + 1/4 sec^2 30^@`
= `(sin^2 28^@ + cos^2 28^@) + tan^2 38^@ - tan^2 38^@ + 1/4 xx (2/sqrt3)^2`
= `1 + 0 + 1/4 xx 4/3`
= `1 + 1/3`
= `4/3`
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