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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 6 Trigonometry Ex 6.1

**9th Maths Trigonometry Exercise 6.1 Question 1.**

From the given figure find all the trigonometric ratios of angle B.

Solution:

**9th maths trigonometry exercise 6.1 Question 2.**

From the given figure, find the values of

(i) sin B

(ii) sec B

(iii) cot B

(iv) cos C

(v) tan C

(vi) cosec C

Solution:

**trigonometry exercise 6.1 Question 3.**

If 2 cos θ = \(\sqrt{3}\), then find all the trigonometric ratios of angle θ.

Solution:

Trigonometry solutions exercise 6.1 Question 4.

If cos A = \(\frac{3}{5}\), then find the value of \(\frac{\sin A-\cos A}{2 \tan A}\)

Solution:

**trignometry solution of 9th class Question 5.**

If cos A = \(\frac{2 x}{1+x^{2}}\) then find the values of sin A and tan A in terms of x.

Solution:

**9th Maths Exercise 6.1 Samacheer Kalvi Question 6.**

Solution:

**9th Maths Exercise 6.1 Question 7.**

If 3 cot A = 2, then find the value of \(\frac{4 \sin A-3 \cos A}{2 \sin A+3 \cos A}\)

Solution:

**9th Std Maths Trigonometry Question 8.**

If cos θ : sin θ = 1 : 2, then find the value of \(\frac{8 \cos \theta-2 \sin \theta}{4 \cos \theta+2 \sin \theta}\)

Solution:

**9th Maths Exercise 6.1 Solution Question 9.**

From the given figure, prove that θ + ϕ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ϕ

Solution:

(∴ By Pythagoras theorem, in a right angled triangle square of hypotenuse is equal to sum of the squares of other two side)

And also in the figure, ∆ADC, ∆DBC are two other triangles.

As per the data given,

9^{2}+ 12^{2} = 81 + 144 = 225 = 15^{2}

∴ ∆ ADC is a right angled triangle, then 12^{2} + 16^{2} = 144 + 256 = 400 = 20^{2}

∴ ∆ DBC is also a right angled triangle

**9th Maths Trigonometry Question 10.**

A boy standing at point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5 m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios)

Solution:

In the figure,

∆OPM, ∆OQN are similar triangles. In similar triangles the sides are in the same proportional.