 # ML Aggarwal Solutions Class 10 Mathematics Solutions for Trigonometric Identities Exercise 18 in Chapter 18 - Trigonometric Identities

Question 1 Trigonometric Identities Exercise 18

If A is an acute angle and sin A = 3/5, find all other trigonometric ratios of angle A (using trigonometric identities).

Solution:

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle. sin A = 3/5 and A is an acute angle

So, in ∆ABC we have ∠B = 90o

And,

AC = 5 and BC = 3

By Pythagoras theorem,

AB = √(AC2 – BC2)

= √(52 – 32) = √(25 – 9) **= √**16

= 4

Now,

cos A = AB/AC = 4/5

tan A = BC/AB = 3/4

cot A = 1/tan θ = 4/3

sec A = 1/cos θ = 5/4

cosec A = 1/sin θ = 5/3

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