1/1+cos^2 thetha + 1/1+sin^2 theta + 1/1+sec^2 theta + 1/1+cosec^2 theta = 2
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Answer: LHS: = 1/1+cos^2 theta + 1/1+sin^2 theta + 1/1+sec^2theta + 1/1+ cosec^2 theta = 1/1+cos^2 theta + 1/1+sin^2 theta + 1/1+1/ cos^2 theta + 1/1+1/sin^2 theta =1/1+cos^2 theta + 1/1+sin^2 theta + 1/cos^2theta+1/ cos^theta + 1/sin^2theta+1/sin^2 theta =1/1+cos^2theta+ 1/1+sin^2theta + cos^2theta/ cos^2theta +1 + sin^2theta / sin^2theta +1 = [ 1/1+cos^2 theta + cos^2theta/ 1+cos^2theta ] + [ 1/1+sin^2theta + sin^2theta/ 1+sin^2theta ] = [ 1+cos^2theta / 1+cos^2 theta ] + [ 1+ sin^2theta/ 1+sin^2theta]. = 1+1 = 2 = RHS. ( Concept used: cosec^2theta= 1/sin^2 theta, sec^2theta = 1/cos^2 theta)
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