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Sign of Trigonometric Ratios in Different Quadrants

Question 1sin...

Question

Question 1
$\frac{s i n θ}{1 + c o s θ} + \frac{1 + c o s θ}{s i n θ} = 2 c o s e c θ$

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Solution

LHS $= \frac{s i n θ}{1 + c o s θ} + \frac{1 + c o s θ}{s i n θ} = \frac{s i n^{2} θ + (1 + c o s θ)^{2}}{s i n θ (1 + c o s θ)}$

$= \frac{s i n^{2} θ + 1 + c o s^{2} θ + 2 c o s θ}{s i n θ (1 + c o s θ)} [∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b]$

$= \frac{1 + 1 + 2 c o s θ}{s i n θ (1 + c o s θ)} [∵ s i n^{2} θ + c o s^{2} θ = 1]$

$= \frac{2 (1 + c o s θ)}{s i n θ (1 + c o s θ)} = \frac{2}{s i n θ}$

$= 2 c o s e c θ = R H S [c o s e c θ = \frac{1}{s i n θ}]$

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Similar questions

Q. Question 10
If

s i n θ + c o s θ = p

s e c θ + c o s e c θ = q

, then prove that

q (p^{2} - 1) = 2 p

Q. Question 5
If

s i n θ + 2 c o s θ = 1

, then prove that

2 s i n θ - c o s θ = 2

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Sign of Trigonometric Ratios in Different Quadrants

Standard XII Mathematics

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