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RD Chapter 6 Trigonometric Identities Ex 6.1 Solutions

Question - 1 : - Prove the following trigonometric identities :
(1 – cos2 A) cosec2 A = 1

Answer - 1 : -

(1 – cos2 A)cosec2 A = 1
L.H.S. = (1 – cos2 A) cosec2 A = sin2 Acosec2 A  (∵ 1 – cos2 A = sin2 A)
= (sin A cosec A)2 = (l)2 = 1 = R.H.S. {sin A cosec A = 1 }

Question - 2 : - (1 + cot2 A) sin2 A = 1

Answer - 2 : -

(1 + cot2 A)sin2 A = 1
L.H.S. = (1 + cot2 A) (sin2 A)
= cosec2 A sin2 A {1 + cot2 A =cosec2 A}
= [cosec A sin A]2
= (1)2= 1 = R.H.S. (∵sin A cosec A = 1

Question - 3 : - tan2 θ cos2  θ = 1- cos2  θ

Answer - 3 : -

Question - 4 : -

Answer - 4 : -


Question - 5 : - (sec2 θ – 1) (cosec2 θ – 1) = 1

Answer - 5 : -


Question - 6 : -

Answer - 6 : -


Question - 7 : -

Answer - 7 : -


Question - 8 : -

Answer - 8 : -


Question - 9 : -

Answer - 9 : -


Question - 10 : -

Answer - 10 : -


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