Example 9 - Chapter 8 Class 10 Introduction to Trignometry

Transcript

Example 9 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 −𝒔𝒊𝒏𝟐 𝑨) Here, A is acute (i.e. less than 90°) & cos A is positive when A is acute So, cos A = √(𝟏 −𝒔𝒊𝒏𝟐 𝑨) sec A sec A = 1/cos⁡〖 𝐴〗 sec A = 𝟏/√(𝟏 −𝒔𝒊𝒏𝟐 𝑨) tan A We know that tan A = 𝑠𝑖𝑛⁡〖 𝐴〗/𝑐𝑜𝑠⁡〖 𝐴〗 Putting value of cos A tan A = 𝒔𝒊𝒏⁡〖 𝑨〗/√(𝟏 − 𝒔𝒊𝒏𝟐 𝑨)