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If sec tetha+tan tetha=p, prove that sin tetha=p²-1/p²+1 |
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Answer» Step-by-step explanation:sec θ + tan θ = p(a + b)² = a² + b² + 2absec²θ - 1 = tan²θtan²θ + 1 = sec²θtan θ = sinθ/cos θ1/ sec θ = cos θWe know that sec θ + tan θ = p.We have to prove that,Taking the RHS of the above equation,Substitute the VALUE of p from given,EXPANDING by using identities,Again APPLYING identities,Taking 2 tanθ COMMON from numerator and 2 secθ common from denominator,CANCELLING tanθ + sec theta and 2 on both numerator and denominator,= sin θ Hence LHS = RHSHence proved. |
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