Question

prove the following :-





(class 10 cbse )

Answer 1

hope it will help you

Answer 2

hey !!!

sec¢ - tan¢ = x --------1)

then ,

just like using rationalising process ( class9th )

1/ x = 1/sec¢ - tan¢ × sec¢ + tan¢ /sec¢ + tan¢

1/x = sec¢ + tan¢ / sec²¢ - tan²¢

As we know that ,

sec²¢ - tan²¢ = 1

so , 1/x = sec¢ + tan¢ /1 = sec¢ - tan¢

1/x = sec¢ + tan¢ --------2

if we adding the both equation

we got ,

1/x + x = sec¢ + tan¢ +sec¢ - tan¢

1/x + x = 2sec¢

sec¢ = 1/2(1/x + x) 1st prooved ..

similarly ,

if we substracting from equ 1 to 2, we got

sec¢ + tan¢ -( sec¢ - tan¢ ) = 1/x - x

2tan¢ = 1/x - x

tan¢ = 1/2 (x + 1/x- x) prooved 2nd one

hope it helps !!!!

₹Rajukumar111 :-D@@@@@@@@