Question

The value of $x$ which will satisfy the equation:

$x\times cos\left(a\right)\times cos({90}^{\circ }-a)\times tan({90}^{\circ }-a)\times sec\left(a\right)\times cosec\left(a\right)\times tan\left(a\right)=1$ is ___

Answer 1

$As,cos({90}^{\circ }-a)=sinatan({90}^{\circ }-a)=cotaSo,x\times cos\left(a\right)\times cos({90}^{\circ }-a)\times tan({90}^{\circ }-a)\times sec\left(a\right)\times cosec\left(a\right)\times tan\left(a\right)=1\Rightarrow x\times cos\left(a\right)\times sin\left(a\right)\times cot\left(a\right)\times sec\left(a\right)\times cosec\left(a\right)\times tan\left(a\right)=1\Rightarrow x\times \left(cos\right(a)\times sec(a\left)\right)\times \left(sin\right(a)\times cosec(a\left)\right)\times \left(cot\right(a)\times tan(a\left)\right)=1\Rightarrow x\times 1\times 1\times 1=1\Rightarrow x=1$