Math, asked by BrainlyHelper, 1 year ago

Prove the following trigonometric identities. \frac{cosA}{1-tanA}+\frac{sinA}{1-cotA}=sinA+cosA

Answers

Answered by SulagnaRoutray
21

Answer:

Refer to the attachment for your answer.

Attachments:
Answered by nikitasingh79
1

Answer with Step-by-step explanation:

Given:  cosA/(1 − tanA) + sinA /(1 − cotA) = sin A + cosA

LHS : cosA/(1 − tanA) + sinA /(1 − cotA)

= cosA/(1 − sinA/cosA) + sinA/(1 − cosA/sinA)

[By using the identity, cotθ = cosθ/sinθ  ,  tanθ = sinθ/cosθ ]

= cosA/[(cosA− sinA)/cosA)] + sinA/[(sinA − cosA)/sinA]

[By taking LCM]

= cosA × cosA /[(cosA− sinA)] + sinA × sinA / [(sinA − cosA)]

= cos²A/(cosA−sinA) − sin² A /(cosA − sinA)

= (cos²A − sin²A)/(cosA−sinA)

[By taking LCM]

= [(cosA + sinA)(cosA − sinA)] / (cosA − sinA)

[By using identity , a² - b² = (a + b) (a - b)]

= cos A + sin A

cosA  / (1 − tanA) + sinA /(1 − cotA)  = sin A + cosA

L.H.S = R.H.S  

Hence Proved..

HOPE THIS ANSWER WILL HELP YOU...

Similar questions