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If sectheta-tantheta=k,then prove that(k²+1)sintheta=(k²-1) |
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Answer» sectheta-tantheta=ksecθ - tanθ = K To Find : prove that (k²+1)sin θ=(k²-1)Solution:secθ - tanθ = k As we know thatsec²θ - tan²θ =1=> (secθ + tanθ )(secθ - tanθ ) = 1=> (secθ + tanθ )(k ) = 1=> secθ + tanθ = 1/ksecθ - tanθ = k secθ + tanθ = 1/k=> 2secθ = k + 1/k=> secθ = (k² + 1)/2k=> cosθ = 2k/ (k² + 1)2tanθ = 1/k - k=> tanθ = ( 1- k²)/2k(k²+1)sin θ=(k²-1)LHS = (k²+1)sin θ= (k²+1) cosθtan θ= (k²+1) (2k/ (k² + 1)) (( 1- k ²_/2k) = 1- k ²≠RHSproblem in dataif secθ + tanθ = k then it will satisfy as then tanθ = ( k² - 1 )/2kLearn More: If sinθ + cosθ = √2cosθ, (θ ≠ 90°) then the value of tanθ is a) √2 ... brainly.in/question/13094229If 15 tan 0 = 8 Find values of cos 0 & Cosec . - Brainly.inbrainly.in/question/34026772 |
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