Prove that: (cos40° -sin40°)/(cos40°+sin40°) = tan5°
 Answer:

You need to remember that if the questions have no any angle whose value is known to you then, you need to use the sum or difference formula according to the given condition.

Here, we have 40° in the left and 5° in the right!
What if we find difference of both angles? We get 35°, is it known to us? Do we know the value of it? No, we don't! Don't use calculator to guess the value of it!

Now, let's sum those two angles!
We get 45° and of course we know the value of any Trigonometric function at 45°.
But, we can't simply put these values because we have tan on the right while sin and cos on the left
But, what we know is sin divided by cos is tan! So, what if we take 45°-5°= 40°, this will provide us what's needed! I.e. 5° on the right and 40° on the left!
Then we solve using the formula of compound angles!

We have the formula that
Tan(45°-A) = (1-tanA)/(1+tanA)

And, when we apply the simple Mathematics, we come to a solution and therefore, this is the way how you solve the given Trigonometric questions of Mathematics.

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