Question

show that
(Cosec A -sin A)
(sec A-cos A)
(tan A +CotA) = 1​

Answer 1

Step-by-step explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER:-}}\mid}}$

$( \csc(A) - \sin(A) ) \times ( \sec(A) - \cos(A) ) \times (\tan(A) + \cot(A) ) = 1 \\ \\ (\frac{1}{\sin(A)} - \sin(A) ) \times (\frac{1}{\cos(A)} - \cos(A) ) \times (\tan(A) + \frac{1}{\cot(A)} ) \\ \\ (\frac{1 - {\sin}^{2}(A)}{\sin(A)} ) \times (\frac{1 - {\cos}^{2} (A) }{\cos(A) }) \times (\frac{{\tan}^{2} (A) + 1 }{\tan(A)} \\ \\ \frac{{\cos}^{\cancel{2}}(A)}{\cancel{\sin(A)}} \times \frac{{\sin}^{\cancel{2}} (A) }{\cancel{\cos(A)}} \times \frac{{\sec}^{2}(A)}{\frac{\sin(A)}{\cos(A)}} \\ \\ \sin(A) \times \cos(A) \times \frac{\frac{1}{{\cos}^{\cancel{2}} (A) }}{\frac{\sin(A)}{\cancel{\cos(A)}}} \\ \\ \cancel{\sin(A) \times \cos(A)} \times \frac{1}{\cancel{\sin(A) \times \cos(A})} \\ \\ \implies 1 \\ \\ \huge\bold{\underline{R.H.S}}$