Question

(1+cot^2A) sin^2A =1​

Answer 1

To Prove:-

• $\tt (1+\cot^2 A )\sin^2 A=1$

Solution:-

We know this identity

$\tt \csc^2 A=1+\cot^2 A \rightarrow\rightarrow \rightarrow \rightarrow(1)$

Equating LHS first

So putting the value of cosec A in the Question

$\tt (1+\cot^2 A )\sin^2 A \\\\ \tt = \csc^2 A \times \sin^2A \rightarrow \rightarrow \rightarrow \rightarrow(2)$

We also know

$\tt \csc A = \dfrac{1}{\sin A}$

So putting value of cosec in equation (2)

$\tt \dfrac{1}{\sin^2A} \times \sin^2 A \\\\ \tt = \dfrac{1}{\cancel{\sin^2A}} \times \cancel{\sin^2 A} \\\\ \tt =1$

So, LHS = RHS

proved

Other Trigonometrical identities:-

• $\tt \sin^2A+\cos^2A = 1$

• $\tt \sec^2A=1+\tan^2A$