Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Ex 8.3

Ex 8.3, 1

Ex 8.3, 2 Important

Ex 8.3, 3 (i) [MCQ]

Ex 8.3, 3 (ii) [MCQ] Important

Ex 8.3, 3 (iii) [MCQ] Important

Ex 8.3, 3 (iv) [MCQ]

Ex 8.3, 4 (i) Important

Ex 8.3, 4 (ii)

Ex 8.3, 4 (iii) Important

Ex 8.3, 4 (iv) Important

Ex 8.3, 4 (v) Important

Ex 8.3, 4 (vi)

Ex 8.3, 4 (vii) Important

Ex 8.3, 4 (viii) You are here

Ex 8.3, 4 (ix) Important

Ex 8.3, 4 (x)

Question 1 (i) Important Deleted for CBSE Board 2024 Exams

Question 1 (ii) Deleted for CBSE Board 2024 Exams

Last updated at Aug. 16, 2023 by Teachoo

Ex 8.3, 4 Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A Solving L.H.S (sin A + cosec A)2 + (cos A + sec A)2 = (sin2 A + cosec2 A + 2sin A cosec A) + (cos2 A + sec2 A + 2 cos A . sec A) = (sin2 A + cosec2 A + 2sin A . 1/sin〖 𝐴〗 ) + (cos2 A + sec2 A + 2 cos A.1/cos〖 𝐴〗 ) = (sin2 A + cosec2 A + 2) + (cos2 A + sec2 A + 2) Using cosec2 A = 1 + cot2 A sec2 A = 1 + tan2 A = (sin2 A + (1 + cot2 A) +2) + (cos2 A + (1 + tan2 A) + 2) = sin2 A + cos2 A + 1 + cot2 A + 2 + 1 + tan2 A + 2 = (sin2 A + cos2 A) + cot2 A + tan2 A + (1 + 2 + 1 + 2) = sin2 A + cot2 A + 1 + 2 + cos2 A + 1 + tan2 A + 2 = (sin2 A + cos2 A) + cot2 A + tan2 A + (1 + 2 + 1 + 2) Using sin2 A + cos2 A = 1 = 1 + cot2 A + tan2 A + 6 = 7 + cot2 A + tan2 A = R.H.S Hence proved = sin2 A + cot2 A + 1 + 2 + cos2 A + 1 + tan2 A + 2 = (sin2 A + cos2 A) + cot2 A + tan2 A + (1 + 2 + 1 + 2) Using sin2 A + cos2 A = 1 = 1 + cot2 A + tan2 A + 6 = 7 + cot2 A + tan2 A = R.H.S Hence proved