Question

Prove that ,sintheta (1+tantheta)+costheta(1+cottheta)=sectheta+cosectheta.​

Answer 1

Answer:

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Answer 2

=> sinx[1 + sinx /cosx ]  + cosx [1+ cosx / sinx ]

=> sinx [ cosx + sinx /cosx ] +cosx [ sinx + cosx /sinx ]

=> [sinx + cosx] [ sin^2x + cos^2x /sinxcosx ]

now as we know that sin^2x+ cos^2x = 1

now,

=> [sinx + cosx ] [ 1 /sinxcosx ]

=> [sinx  + cosx / sinxcosx]

=> 1 /cosx + 1 / sinx  

=> secx + cosecx

Hope that it is helpful to you

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