sin ( 1+ tan) + cos(1+cos) =sec+ cosec
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sin (1 + tan) + cos (1 + cot) = sec + cosec
Left Hand Side
= sin (1 + tan) + cos (1 + 1 ÷ tan)
= sin (1 + tan) + cos (1 + tan) ÷ tan
= (1 + tan)(sin + cos ÷ tan)
= (1 + tan)(sin × tan + cos) ÷ tan
= (1 + tan)(sin^2 ÷ cos + cos) ÷ tan
= (1 + tan)(sin^2 + cos^2) ÷ tan × cos
= (1 + tan) ÷ tan × cos
= (1 ÷ tan × cos) + tan ÷ tan × cos
= ( cot ÷ cos) + (1 ÷ cos)
= cosec + sec [LHS = RHS] (PROVED)
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