Trigonometric Functions Short Questions (Question 11 - 14)


Question 11:
Prove the identity  cos 2 x 1sinx =1+sinx
Solution:
LHS = cos 2 x 1sinx = 1 sin 2 x 1sinx sin 2 x+ cos 2 x=1 = ( 1+sinx )( 1sinx ) 1sinx =1+sinx =RHS Proven


Question 12:
Prove the identity  sin 2 x cos 2 x= tan 2 x1 tan 2 x+1
Solution:
RHS = tan 2 x1 tan 2 x+1 = sin 2 x cos 2 x 1 sin 2 x cos 2 x +1 tanx= sinx cosx = sin 2 x cos 2 x cos 2 x sin 2 x+ cos 2 x cos 2 x = sin 2 x cos 2 x sin 2 x+ cos 2 x = sin 2 x cos 2 x sin 2 x+ cos 2 x=1 =LHS Proven


Question 13:
Prove the identity  tan 2 θ sin 2 θ= tan 2 θ sin 2 θ
Solution:
LHS = tan 2 θ sin 2 θ = sin 2 θ cos 2 θ sin 2 θ = sin 2 θ sin 2 θ cos 2 θ cos 2 θ = sin 2 θ( 1 cos 2 θ ) cos 2 θ = sin 2 θ sin 2 θ cos 2 θ =( sin 2 θ cos 2 θ )( sin 2 θ ) = tan 2 θ sin 2 θ =RHS Proven


Question 14:
Prove the identity cosec 2 θ ( sec 2 θ tan 2 θ )1= cot 2 θ
Solution:
LHS = cosec 2 θ ( sec 2 θ tan 2 θ )1 = cosec 2 θ ( 1 )1 tan 2 θ+1= sec 2 θ sec 2 θ tan 2 θ=1 = cosec 2 θ1 = cot 2 θ 1+ cot 2 θ=cose c 2 θ cose c 2 θ1= cot 2 θ =RHS Proven