Question

$cos^{2}67-sin^{2}23\\\\show working also$

Answer 1

Hey there!

The given trigonometric function with value is;

$\bf{cos^2(67) - sin^2(23)}$

By the basic principles for a identity rule for trigonometric functions for "cos" that is,

$\bf{Therefore, \: cos(x) = sin(90 - x)}$

$\bf{Here, \: cos(67) = sin(90 - 67)}$

Now, just apply the trigonometric identity into our original values of trigonometric equation.

$\bf{\therefore \quad sin^2(90 - 67) - sin^2(23)}$

$\bf{\therefore \quad sin^2(23) - sin^2(23)}$

Add the similar elements or same trigonometric values to obtain the final answer.

$\boxed{\bf{\underline{\therefore \quad cos^2(67) - sin^2(23) = 0}}}$

Which is the required answer or the final solution for these types of queries.

Hope this helps you and clears your doubts for applying trigonometric identities into the given equational values !!!!