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ML Aggarwal Solutions Class 10 Mathematics Solutions for Trigonometric Identities Exercise 18 in Chapter 18 - Trigonometric Identities
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Question 35 Trigonometric Identities Exercise 18
If sin θ + cos θ = √2 sin (90° – θ), show that cot θ = √2 + 1
Answer:
Solution:
In RHS, first we can apply complementary trignometric angles concept
Given, sin θ + cos θ = √2 sin (90° – θ)
sin θ + cos θ = √2 cos θ
On dividing by sin θ, we have
1 + cot θ = √2 cot θ
1 = √2 cot θ – cot θ
(√2 – 1) cot θ = 1
cot θ = 1/ (√2 – 1)
=\frac{1 \times(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)} (Rationalising the denominator)
\begin{aligned} &=\frac{(\sqrt{2}+1)}{(\sqrt{2})^{2}-(1)^{2}}=\frac{\sqrt{2}+1}{2-1}=\frac{\sqrt{2}+1}{1} \\ &=\sqrt{2}+1=\text { R.H.S. } \end{aligned}
Hence, cot θ = √2 + 1
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