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Example 12 - Express cos A, tan A and sec A in terms of sin A - Expressing ratios in other ratios

Example 12 - Chapter 8 Class 10 Introduction to Trignometry - Part 2

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Example 12 Express the ratios cos A, tan A and sec A in terms of sin A. cos A Since, cos2 A + sin2 A = 1 cos2 A = 1 – sin2 A cos A = ±√(1 βˆ’π‘ π‘–π‘›2 𝐴) Here, A is acute (i.e. less than 90Β°) & cos A is positive when A is acute So, cos A = √(1 βˆ’π‘ π‘–π‘›2 𝐴) sec A sec A = 𝟏/πœπ¨π¬β‘γ€– 𝑨〗 sec A = 1/√(1 βˆ’π‘ π‘–π‘›2 𝐴) tan A We know that tan A = π’”π’Šπ’β‘γ€– 𝑨〗/𝒄𝒐𝒔⁑〖 𝑨〗 Putting value of cos A tan A = sin⁑〖 𝐴〗/√(1 βˆ’ 𝑠𝑖𝑛2 𝐴)

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