Question

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Answer 1

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

Answer 2

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 )