Question

Please please please prove This soon​

Answer 1

Explanation:

LHS

sec@ + tan@

1/cos@ + sin@/cos@

(1 + sin@)/cos@

we know that

cos(π/2 - @) = sin@

sin(π/2 - @) = cos@

we also know that

according to half angle trigonometry formula.

1 + cos@ = 2cos^2@/2

sin@ = 2cos @/2 sin@/2

Now

{1 + cos(π/2 - @)}/sin(π/2 - @)

2cos^2 (π/4 - @/2)/2 sin(π/4- @/2)cos(π/4 -@/2)

cos(π/4 - @/2)/sin (π/4 - @/2)

we also know that

cos(π/4 - @/2)/sin (π/4 - @/2)=( cos@)2 + sin@/2)/(sin@ /2- cos@/2)

so

we also write as

sin(π/4 + π/2)/cos(π/4 + @/2)

tan(π/4 + @/2)

hence

LHS = RHS

proved