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A,B,C are interior angles if triangle..
.therefore A+B+C=180....
B+C=180-A.....①
question......tan²((B+C)/2)=cosec2A/2-1
LHS
tan²((180-A)/2)
tan²(90-A/2)
cot²(A/2).............(tan(90-theta)=cot(theta)
cosec²A/2-1......(cot²theta=cosec²theta-1)=RHS....
hence proved....
.therefore A+B+C=180....
B+C=180-A.....①
question......tan²((B+C)/2)=cosec2A/2-1
LHS
tan²((180-A)/2)
tan²(90-A/2)
cot²(A/2).............(tan(90-theta)=cot(theta)
cosec²A/2-1......(cot²theta=cosec²theta-1)=RHS....
hence proved....
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