The value of the expression 3 20^ - 4 20^ is equal to :

Step-by-step solution

The given expression is 3 20^ - 4 20^ . Converting cotangent to sine and cosine: = 3 20^ 20^ - 4 20^ = 3 20^ - 4 20^ 20^ 20^ Using the double angle formula 2 = (2 ) in the second term of the numerator: = 3 20^ - 2 40^ 20^ Substitute 3 = 2 60^ : = 2 60^ 20^ - 2 40^ 20^ Using the product-to-sum formula 2 A B = (A+B) + (A-B) : 2 60^ 20^ = (60^ + 20^ ) + (60^ - 20^ ) = 80^ + 40^ Substituting this back into the numerator: = 80^ + 40^ - 2 40^ 20^ = 80^ - 40^ 20^ Now, apply the sum-to-product formula C - D = 2 ( C+D 2 ) (