Last updated at Dec. 24, 2019 by Teachoo

Transcript

Ex 8.4, 4 Choose the correct option. Justify your choice. (i) 9 sec2 A – 9 tan2 A 1 (B) 9 (C) 8 (D) 0 9 sec2 A – 9 tan2 A = 9 (1 + tan2 A) – 9 tan2 A = 9 + 9 tan2 A – 9 tan2 A = 9 + 0 = 9 Hence B is the correct option Ex 8.4, 4 Choose the correct option. Justify your choice. (ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ) (A) 0 (B) 1 (C) 2 (D) –1 (1 + tan θ + sec θ) (1 + cot θ – cosec θ) Writing in terms of sin θ & cos θ = (1+" " sin𝜃/cos𝜃 " + " 1/cos𝜃 " " ) (1+" " cos𝜃/sin𝜃 " − " 1/sin𝜃 " " ) = ((cos𝜃 +sin𝜃 + 1))/cos𝜃 × ((sin𝜃 +cos𝜃 − 1))/sin𝜃 = (({cos𝜃 +sin𝜃 } + 1) ({sin𝜃 +cos𝜃 }− 1))/(cos𝜃 sin𝜃 ) = ( (cos𝜃 +sin𝜃 )2 −12)/(cos𝜃 sin𝜃 ) = (𝑐𝑜𝑠2 𝜃 + 𝑠𝑖𝑛2 𝜃 +2 cos𝜃 sin𝜃 − 1)/(cos𝜃 sin𝜃 ) = (1 + 2 cos𝜃 sin𝜃 − 1)/(cos𝜃 sin𝜃 ) = (2 cos𝜃 sin𝜃)/(cos𝜃 sin𝜃 ) = 2 Answer = 2 Hence, option (B) is correct. Ex 8.4, 4 Choose the correct option. Justify your choice. (iii) (sec A + tan A) (1 – sin A) sec A (B) sin A (C) cosec A (D) cos A (sec A + tan A) (1 – sin A) = (1/(𝑐𝑜𝑠 𝐴)+sin𝐴/cos〖 𝐴〗 ) (1 −sin〖 𝐴)〗 = ((1+ sin〖 𝐴)〗)/cos〖 𝐴〗 ×(1 −sin〖 𝐴)〗 = ((1+ sin〖 𝐴)(1 −〖 sin〗〖 𝐴)〗 〗)/cos〖 𝐴〗 = ((1^2 −〖 sin2〗〖 𝐴)〗)/cos〖 𝐴〗 = ((1 −〖 sin2〗〖 𝐴)〗)/cos〖 𝐴〗 = (𝑐𝑜𝑠2 𝐴)/cos〖 𝐴〗 = cos A Hence, (D) is the correct answer Ex 8.4, 4 Choose the correct option. Justify your choice. (iv) (1 + 𝑡𝑎𝑛2𝐴)/(1 + 𝑐𝑜𝑡2𝐴) sec2 A (B) –1 (C) cot2 A (D) tan2 A (1 + 𝑡𝑎𝑛2𝐴)/(1 + 𝑐𝑜𝑡2𝐴) = (1 + 𝑠𝑖𝑛2𝐴/( 𝑐𝑜𝑠2 𝐴))/(1 + 𝑐𝑜𝑠2𝐴/(𝑠𝑖𝑛2 𝐴)) = ((𝑐𝑜𝑠2 𝐴 + 𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴))/((𝑠𝑖𝑛2 𝐴 + 𝑐𝑜𝑠2 𝐴)/𝑠𝑖𝑛2𝐴) = (𝑐𝑜𝑠2 𝐴 + 𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴) × (𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴 + 𝑠𝑖𝑛2 𝐴) = 1/(𝑐𝑜𝑠2 𝐴) × (𝑠𝑖𝑛2 𝐴)/1 = (𝑠𝑖𝑛2 𝐴)/(𝑐𝑜𝑠2 𝐴) = ((𝑠𝑖𝑛 𝐴)/(𝑐𝑜𝑠 𝐴))^2 = tan2 A Answer = tan2 A Hence, option (D) is correct

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.