Question

(sin tita + cosec tita)² + (cos tita _sec tita)² _(tan tita +cot)² = 1​

Answer 1

Here I am using A instead of theta.

LHS = (sinA+cosecA)²+(cosA-secA)²-(tanA+cotA)²

= sin²A+cosec²A+2sinAcosecA+cos²A+sec²A-2cosAsecA-tan²A-cot²A-2tanAcotA

Rearranging the terms , we get

= (sin²A+cos²A)+(cosec²A-cot²A)+(sec²A-tan²A)+2-2-2

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Since ,

i ) sinAcosecA = 1

ii ) cosAsecA = 1

iii ) tanAcotA = 1

iv) sin²A+cos²A = 1

v ) cosec²A-cot²A = 1

vi ) sec²A - tan²A = 1

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= 1+1+1+2-2-2

= 5-4

= 1

= RHS

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