((1+tan^2@)cot@)/cosec^2@=tan@.
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Answer:
( 1 - Tan)² + (1 - Cot)² = (Sec - Cosec)²
Step-by-step explanation:
(1-Tan)^2+(1-Cot)^2=(Sec-Cosec)^2 Prove
LHS
= ( 1 - Tan)² + (1 - Cot)²
= ( 1 - Sin/Cos)² + (1 - Cos/Sin)²
= (Cos - Sin)²/Cos² + (Sin - Cos)²/Sin²
= (Cos - Sin)² ( 1/Cos² + 1/Sin²)
= (Cos - Sin)² (Sin² + Cos²)/Cos²Sin²
= (Cos - Sin)² /Cos²Sin²
= ((Cos - Sin)/CosSin )²
= (Cos/CosSin - Sin/CosSin)²
= (1/Sin - 1/Cos)²
= (Cosec - Sec)²
= (Sec - Cosec)²
= RHS
QED
Proved
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