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^2 A = ( 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

Trigonometric Identity- 2

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

LHS $= (c o s e c A - s i n A) (s e c A - c o s A) s e c^{2} A$
$= (\frac{1}{s i n A - s i n A}) + (\frac{1}{c o s A} - c o s A) \times \frac{1}{c o s^{2} A}$
$= (\frac{1 - s i n^{2} A}{s i n A}) (\frac{1 - c o s^{2} A}{c o s A}) \times \frac{1}{c o s^{2} A}$
$= \frac{c o s^{2} A}{s i n A} \times \frac{s i n^{2} A}{c o s A} \times \frac{1}{c o s^{2} A} = \frac{s i n A}{c o s A}$
$= t a n A =$ RHS
Hence, proved

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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)sec2 A =(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=sin Acos A =tan A=RHS Hence, proved

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]