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ML Aggarwal Solutions Class 9 Mathematics Solutions for Trigonometric Ratios Exercise 17 in Chapter 17 - Trigonometric Ratios
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. If tan = 4/3
find the value of sin .. cos … (both sin and cos are Positive)
Answer:
Let ∆ABC be a right-angled
∠ACB = θ
Given that, tan θ = 4/3
(AB/BC = 4/3)
Give that, tan θ = 4/3
(AB/BC = 4/3)
Let AB = 4x,
then BC = 3x
In right-angled ∆ABC
By Pythagoras theorem, we get
\begin{array}{l} A C^{2}=A B^{2}+B C^{2} \\ A C^{2}=A B^{2}+B C^{2} \\ A C^{2}=A B^{2}+B C^{2} \\ A C^{2}=A B^{2}+B C^{2} \\ \left(A C^{2}=(4 x)^{2}+(3 x)\right. \\ A C^{2}=16 x^{2}+9 x^{2} \\ A C^{2}=25 x^{2} \\ A C^{2}=(5 x)^{2} \\ A C=5 x \end{array}
AC = 5x
Sin θ = perpendicular/Hypotenuse
= AB/AC
= 4x/5x
= 4/5
Cos θ = Base/Hypotenuse
= BC/AC
= 3x/5x
= 3/5
Sin θ + cos θ
= 4/5 + 3/5
= (4 + 3)/5
= 7/5
Hence, Sin θ + cos θ = 7/5 = 1 (2/5)
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