Question

The value of cos ec2 67°-tan2 23°+1 is:​

Answer 1

Answer:

$\large\bold\red{2}$

Step-by-step explanation:

To find the Value of,

${ \csc }^{2}67 - { \tan }^{2} 23 + 1$

We know that,

$\csc( \alpha ) = \sec(90 - \alpha )$

Therefore,

We get,

$\csc(67) = \sec(23)$

Thus,

We get,

$= { \sec }^{2} 23 - { \tan }^{2} 23 + 1$

But,

We know that,

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

Therefore,

We get,

$= 1 + 1 \\ \\ = 2$

Hence,

The value of given expression is 2.