those who will give this answer I will as the brain list please give me this answer
Share
those who will give this answer I will as the brain list please give me this answer
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
QUESTION :tan²X/(secX+1) = (1-cosX)/cosX
ANSWER :
LHS =
tan²X/(secX+1)
= (sec²X-1)/(secX+1) ..............(1+tan²X=sec²X)
=(secX-1)(secX+1)/(secX+1)...........(a²-b²=(a+b)(a-b))
=(secX-1)
=(1/cosX) -1
=(1-cosX)/cosX
=RHS
hence proved
NOTE :
1. IDENTITIES USED :
A) trigonometric identities
a)cosA=(1/secA)
b)1+tan²A=sec²A
B) algebraic identities
a)a²-b²=(a+b)(a-b)
2.ADVICE :
while solving such questions try to convert the equation in simplest form
TO PROVE ,
tan² x / sec x + 1 = 1 - cos x / cos x
PROOF,
tan² x / sec x + 1 = 1 - cos x / cos x
LHS RHS
⇒ sin² x / cos ² / (1/cosx + cos x) = 1 - cos x / cos x
⇒ sin ² x / cos² x /( 1 + cos x / cos x)
⇒ sin² x / cos x / ( 1 + cos x )
⇒sin² x / cosx ( 1+ cos x)
⇒ ( 1 - cos² x ) /cos x ( 1 + cos x)
⇒( 1 - cos x ) ( 1 + cos x) / cos x ( 1 + cos x)
⇒ ( 1 - cos x ) / cos x ( = RHS )
∴ LHS = RHS
( HENCE , PROVED )