Question: If 3 cot A = 4, check whether (1−tan²A)/(1+tan²A) = cos²A - sin²A
Consider the following , where
fig. 1 (drawn from details provided in question)
Important tip: When solving problems of trigonometry, try drawing a right angled triangle with reference to the details given in the question. This can help you visualize and work faster when calculating trigonometric ratios.
Let's start solving this problem by using the given equation and find the values for AB, BC and AC.
Hence, from equation (1) we can say and
Wondering why we have taken "4x" and "3x" here?
Check this video for understanding it.
As we have already done previously in Trigonometry Numerical | PQ = 12cm and PR = 13cm | Find tan P - cot R and Trigonometry Numerical | 15 cot A = 8 | Find the value of sin A and sec A, let's use the value of AB and BC to find the value of AC by applying Pythagoras Theorem.
Now, that we have the values of all the sides of , we'll put the values in LHS and RHS and prove that LHS = RHS. Let's start with LHS.
Firstly finding the value of .
From equation (3) and (4), we can say