Question

find the value of (cos thitha ×tan thitha)^2+(sin thitha ×cot thitha)^2=?​

Answer 1

Answer:

The value of $(\cos(\theta)\times \tan(\theta))^{2} +(\sin(\theta)\times \cot(\theta))^{2}$ is 1.

Step-by-step explanation:

We need to find the value of

$(\cos(\theta)\times \tan(\theta))^{2} +(\sin(\theta)\times \cot(\theta))^{2}$

We know that

$\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}$        

and

$\cot(\theta)=\dfrac{\cos(\theta)}{\sin(\theta)}$

On substituting the expressions for $\tan(\theta)$ and $\cot(\theta)$ in the given expression, we obtain

$(\cos(\theta)\times \tan(\theta))^{2} +(\sin(\theta)\times \cot(\theta))^{2}=\left(\cos(\theta)\times \frac{\sin(\theta)}{\cos(\theta)} \right)^2+\left(\sin(\theta)\times \frac{\cos(\theta)}{\sin(\theta)} \right)^2$

On multiplying the terms in the brackets, we get

$(\sin(\theta))^2+(\cos(\theta))^2$

We know that the value of the above expression is 1.