Question

How do you prove secx+sinx=tanxsinx?

Answer 1

TO PROVE : secx+sinx=tanxsinx


LHS : secx + sinx

RHS : tanxsinx = sin^2x/cosx

= (1- cos^2x)/cosx

= secx - cosx

so, secx + sinx = secx - cosx

=> sinx = -cosx

which is only possible in second and fourth quadrant that too if x is a π/4 in those quadrants.

Let's put x = 3π/4 (say)

it's in 2nd quadrant.

so, sin3π/4 = 1/√2

-cos3π/4 = -(-1/√2) = 1/√2


SO, LHS = RHS


HENCE PROVED.