Question

nove
Prove
that
Sec
sec A (1-sin A)(SecA + tan A)=1​

Answer 1

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

1/COS A(1-SIN A) (1/COS A+ SIN A/COS A)

(1-SIN A/COS A) (1+SIN A/COS A)

(1-SIN A)(1+SIN A)/COS²A

1-SIN²A/COS²A

COS²A/COS²A

1

Answer 2

Step-by-step explanation:

=1/COS A(1-SIN A)(1/COS A+SIN A/COS A)

=1-SIN A/COS A(1+SIN A/COS A)

=(1-SIN A)(1+SIN A)/COS A×COS A

WE KNOW THAT(a-b)(a+b)=a^2+b^2

(=1-SIN A)^2/COS^2 A

=COS^2 A/COS^2 A 1-SIN^2 A=COS^2A

=1