if sec thita + tan thita=p, prove that sin thita=p2-1 divided by p2+1

@mohammad.ibrahim98; correctly answered the question. Good effort!! Keep posting.

Here, Sec 2θ, tan 2θ means Sec2θ, tan2θ. 

  • 6

see...

sec A + tan A = p then, sec A - tan A = 1/p as, sec2A - tan2A = 1

so, solve the equation, to get sec A or tan A then find sin A u 'll get it...

------Alternate------

sec A + tan A = p

=> sec A = p - tan A

now, square both the sides, and convert them into a single ratio like sin A to get its value directly,

  • 3

Given : sec Ɵ + tan Ɵ = p

 To prove :  sin Ɵ  = p2-1 / p2+1

Proof : p2-1 / p2+1

             (sec Ɵ + tan Ɵ ) 2 - 1   /     (sec Ɵ + tan Ɵ) 2 + 1

              sec2Ɵ + tan2Ɵ + 2secƟ tanƟ - 1   /   sec2Ɵ + tan2Ɵ + 2secƟ tanƟ + 1

              (sec2Ɵ - 1) + tan2Ɵ + 2secƟ tanƟ    /     (tan2Ɵ + 1) + sec2Ɵ + 2 secƟ tanƟ

               tan2Ɵ + tan2Ɵ + 2 secƟ tanƟ   /      sec2Ɵ + sec2Ɵ + 2 secƟ tanƟ

                2tanƟ ( tanƟ + secƟ)       /         2secƟ ( secƟ + tanƟ)

                         Tan Ɵ         /       sec Ɵ

                            sinƟ /  cosƟ   *    cos Ɵ

                                        sin Ɵ  = RHS 

Thumbs up plss!!!!!!!!!!!

  • 80

Thanks a lot 4 ur help............

  • -3
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