Prove that cosec A-sin A A-cos A 2 A-tan A -4 MARKS-

Formula: 2 Marks Proof: 2 Marks LHS=(cosec A sin A)(sec A cos A)(sec^2A) = ( 1/sin A sin A ) ( 1/cos A cos A ). 1/cos^2 A = ( 1 sin^2 A/sin A ) ( 1 cos^2 A ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

Prove that co...

Question

Prove that $(c o s e c A - s i n A) (s e c A - c o s A) s e c^{2} A = t a n A$ [4 MARKS]

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Solution

Formula: 2 Marks
Proof: 2 Marks

$L H S = (c o s e c A - s i n A) (s e c A - c o s A) (s e c^{2} A) = (\frac{1}{s i n A} - s i n A) (\frac{1}{c o s A} - c o s A) . \frac{1}{c o s^{2} A} = (\frac{1 - s i n^{2} A}{s i n A}) (\frac{1 - c o s^{2} A}{c o s A}) . \frac{1}{c o s^{2} A} = \frac{c o s^{2} A}{s i n A} . \frac{s i n^{2} A}{c o s A} . \frac{1}{c o s^{2} A} = t a n A = R H S$

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Prove that (cosec A−sin A)(sec A−cos A) sec2 A=tan A [4 MARKS]

Formula: 2 Marks Proof: 2 Marks LHS=(cosec A−sin A)(sec A−cos A)(sec2A)=(1sin A−sin A)(1cos A−cos A).1cos2 A=(1−sin2 Asin A)(1−cos2 Acos A).1cos2 A=cos2 Asin A.sin2 Acos A.1cos2 A=tan A=RHS

Prove that $(c o s e c A - s i n A) (s e c A - c o s A) s e c^{2} A = t a n A$ [4 MARKS]