Prove the identity- tan-sin 3 -cos-sin-cos-1 -4 MARKS-

Formula: 2 Marks Proof: 2 Marks LHS=tan θ/sin^3 θ/cos θ+sin θ cos θ= tan θ/sin θ ( sin^2θ/cos θ +cos θ ) =tan θ/sin θ(sin^ θ+cos^2 θ)/cos θ=tan θ/tan θ× 1=1=R ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

Prove the ide...

Question

Prove the identity: $\frac{t a n θ}{\frac{s i n^{3} θ}{c o s θ} + s i n θ c o s θ} = 1$ [4 MARKS]

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Solution

Formula: 2 Marks
Proof: 2 Marks

$L H S = \frac{t a n θ}{\frac{s i n^{3} θ}{c o s θ} + s i n θ c o s θ} = \frac{t a n θ}{s i n θ (\frac{s i n^{2} θ}{c o s θ} + c o s θ)} = \frac{t a n θ}{\frac{s i n θ (s i n θ + c o s^{2} θ)}{c o s θ}} = \frac{t a n θ}{t a n θ \times 1} = 1 = R H S$

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