Question 12 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at July 21, 2023 by Teachoo

(sec A + tan A) (1 – sin A) equals:

(a) sec A (b) sin A (c) cosec A (d) cos A

This question is similar to Example 10 - Chapter 8 Class 10 Introduction to Trignometry

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Transcript

(sec A + tan A)(1 – sin A) We write everything in terms of sin A and cos A = (1/cos⁡〖 𝐴〗 +" " sin⁡〖 𝐴〗/cos⁡〖 𝐴〗 ) (1 – sin A) = ((1 +〖 sin〗⁡〖 𝐴〗)/cos⁡〖 𝐴〗 )(1 – sin A) = ((1 +〖 sin〗⁡〖 𝐴) (1 −〖 sin〗⁡〖 𝐴)〗〗)/(cos⁡ 𝐴 ) = ((12 −〖 sin^2〗⁡〖 𝐴) 〗)/( cos⁡〖 𝐴〗 ) = ((𝟏 −〖〖𝒔𝒊𝒏〗^𝟐〗⁡〖 𝑨) 〗)/( 𝒄𝒐𝒔⁡〖 𝑨〗 ) = cos⁡〖2 𝐴〗/( cos⁡〖 𝐴〗 ) = cos A cos2 A + sin2 A = 1 cos2 A = 1 – sin2 A ∴ 1 – sin2 A = cos2 A So, the correct answer is (d)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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