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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).
Answer:
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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