Question

answer this question please

Answer 1

Given, (1+tan^2 theta)(1-sintheta)(1+costheta)

           = (1+tan^2theta)(1-sintheta+costheta - sinthetacostheta)

          = sec^2theta(1-sintheta+costheta - sinthetacostheta)

          = 1/cos^2theta(1-sintheta+costheta - sinthetacostheta)
 
          = 1-sintheta+costheta-sinthetacostheta/(cos^2theta)

          = (sec^2theta-secthetatantheta + sectheta-tantheta)

          = sectheta(sectheta-tantheta)+(sectheta-tantheta)

          = (sectheta+1)(sectheta-tantheta).

Answer 2

hello users ......

we have to simplify:-
( 1 + tan²θ) ( 1 - sin θ) (1 + cos θ) = ? 

solution :-
we know that :
1 + tan²θ = sec² θ

now,
( 1 + tan²θ) ( 1 - sin θ) (1 + cos θ) 
= sec² θ × { 1 + cos θ - sin θ - sin θ cos θ }

= sec² θ + cos θ × sec² θ - sin θ ×sec² θ - sin θ cos θ × sec² θ 

= sec² θ  + sec θ - tan θ sec θ - tan θ 

= sec θ ( sec θ + 1 ) - tan θ ( sec θ + 1 ) 

= ( sec θ - tan θ ) ( sec θ +1 ) answer 

❈❈hope it helps ❈❈