Prove thatsin-1-cos-1-tan-cos-sin-4 MARKS-

Formula: 2 Marks Proof: 2 Marks L.H.S = sin θ/1 cot θ+cos θ/1 tan θ =sin θ/1 cot θ/sin θ+cos θ/1 sin θ/cos θ =sin^2 θ/sin θ cos θ + cos^2 θ/cos θ sin θ =sin^2 ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

Prove thatsin...

Question

Prove that
$\frac{s i n θ}{1 - c o t θ} + \frac{c o s θ}{1 - t a n θ} = c o s θ + s i n θ$ [4 MARKS]

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Solution

Formula: 2 Marks
Proof: 2 Marks

L.H.S $= \frac{s i n θ}{1 - c o t θ} + \frac{c o s θ}{1 - t a n θ}$
$= \frac{s i n θ}{1 - \frac{c o t θ}{s i n θ}} + \frac{c o s θ}{1 - \frac{s i n θ}{c o s θ}}$
$= \frac{s i n^{2} θ}{s i n θ - c o s θ} + \frac{c o s^{2} θ}{c o s θ - s i n θ}$
$= \frac{s i n^{2} θ}{s i n θ - c o s θ} - \frac{c o s^{2} θ}{s i n θ - c o s θ}$
$= \frac{s i n^{2} θ - c o s^{2} θ}{s i n θ - c o s θ}$
$= \frac{(s i n θ + c o s θ) (s i n θ - c o s θ)}{(s i n θ - c o s θ)}$
$= s i n θ + c o s θ =$ RHS

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Prove that sin θ1−cot θ+cos θ1−tan θ=cos θ+sin θ [4 MARKS]

Prove that
$\frac{s i n θ}{1 - c o t θ} + \frac{c o s θ}{1 - t a n θ} = c o s θ + s i n θ$ [4 MARKS]