Trigonometric Functions Short Questions (Question 15 - 18)


Question 15:
Prove the identity  2 cos2A+1 =se c 2 A
Solution:
LHS 2 cos2A+1 = 2 ( 2 cos 2 A1 )+1 cos2A=2 cos 2 A1 = 2 2 cos 2 A = 1 cos 2 A =se c 2 A =RHS Proven 


Question 16:
Prove the identity  2tanA 2se c 2 A =tan2A
Solution:
LHS 2tanA 2se c 2 A = 2tanA 2( tan 2 A+1 ) tan 2 A+1=se c 2 A = 2tanA 1 tan 2 A =tan2A =RHS Proven


Question 17:
Prove the identity tanx+cotx=2cosec 2x
Solution:
LHS =tanx+cotx = sinx cosx + cosx sinx = sin 2 x+ cos 2 x cosxsinx = 1 cosxsinx sin 2 x+ cos 2 x=1 = 1 1 2 sin2x sin2x=2sinxcosx 1 2 sin2x=sinxcosx = 2 sin2x =2( 1 sin2x ) =2cosec 2x =RHS Proven 


Question 18:
Prove the identity  cosxsin2x cos2x+sinx1 = 1 tanx
Solution:
LHS = cosxsin2x cos2x+sinx1 = cosx2sinxcosx ( 12 sin 2 x )+sinx1 cos2x=12 sin 2 x = cosx( 12sinx ) sinx2 sin 2 x = cosx( 12sinx ) sinx( 12sinx ) = cosx sinx =cotx = 1 tanx =RHS Proven