Question

Only for Brainly moderators , Brainly stars and brainly best users ▬▬▬▬ஜ۩۞۩ஜ▬▬(sec a - tan a)^2 (1+sin a)=1-sin a prove it​

Answer 1

Answer:

LHS

(sec a - tan a)² (1+sin a)

= (sec²a + tan²a -2sec a tan a) (1+sin a)

= (1+tan²a+tan²a -2sec a tan a)(1+sin a)

= (1+2tan²a -2sec a tan a)(1+sin a)

tan a = sin a/cos a

16

4.0

= (cos²a + 2sin²a -2sin a)(1+sin a)/cos²a

= (1-sin²a+2sin² a -2sin a)(1+sina)/(1-sin²a) =

= (1+sin²a-2sina)(1+sina) / (1-sin a)(1+sin a) =

= (1-sin a)² (1+sin a)/(1-sin a)(1+sin a) =

= 1-sin a

= RHS

Answer 2

Answer:

LHS

(sec a - tan a)² ( 1+sin a)  

= (sec²a + tan²a -2sec a tan a) (1+sin a)  

= (1+tan²a+tan²a -2sec a tan a)(1+sin a)  

= (1+2tan²a -2sec a tan a)(1+sin a)  

tan a = sin a/cos a  

= (cos²a + 2sin²a -2sin a)(1+sin a)/cos²a

= (1-sin²a+2sin² a -2sin a)(1+sina)/(1-sin²a)  

= (1+sin²a-2sina)(1+sina) / (1-sin a)(1+sin a)  

= (1-sin a)² (1+sin a)/(1-sin a)(1+sin a)  

= 1-sin a  

= RHS

Step-by-step explanation:

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