If sin A - cos A and tan A are in geometric progression- then 6 A - 2 A is equal toA- None of theseB- -1C- 0D- 1

The correct option is D 1 Since sin A, cos A and tan a are in G.P., we have cos^2A=sin A tan A ⇒ cos^3 A=sin^2A ⇒ cot^2A=sec A ⇒ cot^4 A=1+tan^2 A ⇒ cot^6 A co ...

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Standard XII

Mathematics

Basic Trigonometric Identities

If sin A , co...

Question

If sin A, cos A and tan A are in geometric progression, then $c o t^{6} A - c o t^{2}$ A is equal to

-1

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None of these

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Solution

The correct option is C
1

Since sin A, cos A and tan a are in G.P., we have

$c o s^{2} A = s i n A t a n A \Rightarrow c o s^{3} A = s i n^{2} A \Rightarrow c o t^{2} A = s e c A \Rightarrow c o t^{4} A = 1 + t a n^{2} A \Rightarrow c o t^{6} A - c o t^{2} = 1$

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If sin A, cos A and tan A are in geometric progression, then cot6A−cot2 A is equal to

The correct option is C 1 Since sin A, cos A and tan a are in G.P., we have cos2A=sin A tan A⇒cos3 A=sin2A⇒cot2A=sec A⇒cot4 A=1+tan2A⇒cot6 A−cot2=1

If sin A, cos A and tan A are in geometric progression, then $c o t^{6} A - c o t^{2}$ A is equal to

The correct option is C
1

Since sin A, cos A and tan a are in G.P., we have

$c o s^{2} A = s i n A t a n A \Rightarrow c o s^{3} A = s i n^{2} A \Rightarrow c o t^{2} A = s e c A \Rightarrow c o t^{4} A = 1 + t a n^{2} A \Rightarrow c o t^{6} A - c o t^{2} = 1$