Question

(1+ tan2

ө) (1+sinө) (1-sinө)=1​

Answer 1

Step-by-step explanation:

LHS:

(1+ tan²ө) (1+sinө) (1-sinө)

Using Identity: 1+ tan²ө = sec²ө,

we get,

( sec²ө)(1+sinө) (1-sinө) ==>

( sec²ө)(1² - sin²ө) [Since (a+b)(a-b) = a²-b²]

That is,

( sec²ө)(1-sin²ө) ==> ( sec²ө)( cos²ө) [ Using Identity: 1-sin²ө = cos²ө ]

==> [ 1/(cos²ө)] ( cos²ө )

Here, cos²ө gets cancelled out, giving,

====> 1.

RHS :

1.

So,

Since 1=1,

LHS = RHS.

Hence, verified.

Hope this helps!!!!