Question

Prove that: sin 0(1 + tan 0) + cos 0(1 + cot 0) = sec 0 + cosec0​

Answer 1

sin (1+tan)+cos (1+cot)=sec+cosec

=> LHS= sin (1+tan)+cos (1+1/tan)

=> sin (1+tan)+cos (1+tan)/tan

=> (1+tan)(sin+cos/tan)

=> (1+tan)(sin.tan+cos)/tan

=> (1+tan)(sin^2/cos+cos)/tan

=> (1+tan)(sin^2+cos^2)/tan.cos

=>(1+tan)/tan.cos

=>(1/tan.cos)+tan/tan.cos

=>( cot/cos)+(1/cos)

=> cosec +sec

LHS= RHS

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