Question

prove that 1 - cos2A / 1 + cos2A = tan^2​

Answer 1

Answer:

thus,proved by using formula for cos2a in terms of cos a and sina

Answer 2

Given:

A trigonometric equation (1-cos2A)/(1+cos2A) = Tan²A.

To Find:

The proof of LHS = RHS.

Solution:

The given problem can be solved using trigonometric identities.

1. The identities used to prove the given equation are:

• cos2A = cos²A - sin²A
• sin²A + cos²A = 1

2. Using the above identities the given equation can be proved.

=> Consider the LHS of the given equation,

=> (1 - cos2A)/(1 + cos2A),

=> (1 - (cos²A - sin²A) ) / (1 + (cos²A - sin²A) ),

=> (1 - cos²A + sin²A) ) / (1 + cos²A - sin²A ),

=> (sin²A + sin²A) ) / (cos²A+cos²A),

=> (2sin²A)/(2cos²A),

=> (sin²A)/(cos²A) = tan²A = RHS.

=> Hence proved.

Therefore, the given equation is correct and is proved.