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\frac { \operatorname { cot } \theta + \operatorname { cosec } \theta - 1 } { \operatorname { cot } \theta - \operatorname { cosec } \theta + 1 } = \frac { 1 + \operatorname { cos } \theta } { \operatorname { sin } \theta } |
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Answer» Put theta = aCot a-1+cosec a/cot a +1-cosec a= (cot a+cosec a)-1/cot a-cosec a+1=cot a +cosec a- (cosec^2a-cot^2a)/cot a - cosec a+1=(cot a+cosec a)-(cot a+cosec a)(cosec a-cot a)/cot a-cosec a+1=(cot a+cosec a)[1-(cosec a-cot a)]/cot a-cosec a+1=(cot a+cosec a)(1+cot a-cosec a)/cot a- cosec a+1=cot a +cosec a=(cos a/sin a)+1/sin a=1+cos a/sin a |
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