Question

5. Prove the following.
(2) (sece + tane) (1 - sine) = cose​

Answer 1

Answer:

Step-by-step explanation:

To Prove : - (sec A + tan A)(1 - sin A) = cos A

Proof :- LHS,

(sec A + tan A)(1 - sin A)

WE KNOW THAT,

sec A = 1/cos A

tan A = sin A/cos A

SO,

[(1/cos A) + (sin A + cos A)] (1-sin A)

[(1 + sin A)/cos A] (1- sin A)

[1 - sin²A/cos A]                                        [(1+sin A) (1-sin A) = 1- sin²A]

cos²A/cos A                                              [sin²A + cos²A = 1]

cos A

RHS,

cos A

LHS = RHS