Prove the following trigonometric identities:
(secA-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA
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(secA - cosecA)( 1+ tanA +cotA) = tanA secA - cotA cosecA proved
Step-by-step explanation:
To prove: (secA - cosecA) ( 1+ tanA + cotA ) = tanA secA - cotA cosecA
Proof:
LHS = (secA-cosecA)(1+tanA+cotA)
= SecA + SecA. TanA + SecA. CotA - CosecA - CosecA. TanA - CosecA.CotA
= 1/CosA + SecA. TanA + 1/CosA . CosA/SinA - 1/SinA - 1/SinA. SinA/CosA. - CosecA. CotA
= 1/CosA + TanA. SecA + 1/SinA - 1/SinA - 1/CosA - CotA. CosecA
= TanA. SecA - CotA. CosecA
= RHS
RHS = LHS
Hence proved.
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