Question

if sin square theta into cos square theta into 1 + tan squared theta into 1 + cot square theta is equal to X find the value of x​

Answer 1

Answer:

1

Step-by-step explanation

=sin²A * cos²A * (1+tan²A) * (1+cot²A)

[(1+tan²A) = sec²A , (1+cot²A) = cosec²A)]

=sin²A * cos²A * sec²A * cosec²A

=1

Answer 2

Answer:

$\bold\red{x=1}$

Step-by-step explanation:

For simplicity, let's denote theta as alpha .

Given,

${ \sin }^{2} \alpha \times { \cos}^{2} \alpha \times (1 + { \tan }^{2} \alpha ) \times (1 + { \cot}^{2} \alpha ) = x$

But,

we know that,

$1 + { \tan }^{2} \alpha = { \sec}^{2} \alpha$

and,

$1 + { \cot }^{2} \alpha = { \cosec}^{2} \alpha$

So, putting the values,

we get,

$x = ( { \sin }^{2} \alpha \times { \cosec }^{2} \alpha) \times ( { \cos}^{2} \alpha \times { \sec}^{2} \alpha )$

But,

$\sin( \alpha ) = \frac{1}{ \cosec( \alpha ) }$

and,

$\cos( \alpha ) = \frac{1}{\sec( \alpha )}$

So,

Putting the values,

we get,

$\bold{x = 1}$