CUET Preparation Today
If $tan^2θ = 1-a^2$, then the value of $secθ+ tan^3θ cosecθ$ is: |
$(2-a)^{\frac{3}{2}}$ $(a^2-1)^{\frac{3}{2}}$ $(2-a^2)^{\frac{3}{2}}$ $a^{\frac{3}{2}}$ |
$(2-a^2)^{\frac{3}{2}}$ |
$secθ+ tan^3θ cosecθ$ = \(\frac{1}{cosθ}\) + \(\frac{sin3θ}{cos3θ}\) × \(\frac{1}{sinθ}\) = \(\frac{1}{cosθ}\) [ 1 + \(\frac{sin2θ}{cos2θ}\) ] = \(\frac{1}{cosθ}\) [ \(\frac{ cos2θ + sin2θ }{cos2θ}\) ] = \(\frac{1}{cosθ}\) × \(\frac{ 1 }{cos2θ}\) = \(\frac{ 1 }{cos3θ}\) = sec3θ As ,tan2θ = 1 - a2 sec2θ - 1 = 1 - a2 ( tan2θ = sec2θ - 1 ) sec2θ = 2 - a2 sec3θ = $(2-a^2)^{\frac{3}{2}}$ |
