Derive the expression 1 + tan2x.
Answer: The expression 1 + tan2x can be expressed as 1 + tan2x = sec2x
Let us proceed step by step to get the required expression.
sin2x + cos2x = 1 ——- (i)
Dividing both sides of the equation by cos2x
(sin2x / cos2x) + (cos2x / cos2x) = 1/cos2x
From trigonometric identity, we already know that
sin2x / cos2 x = tan2x , and cos2x / cos2x = 1
On substituting both the values in eqn (i), we get
tan2x + 1= 1/ cos2x ——–(ii)
Now we know that, 1/ cos2 x = sec2x
On replacing 1/ cos2x with sec2x, equation (ii) becomes tan2x + 1 = sec2x