Question

Which of these are equivalent to 2tanx(sec^2x-1)/cos^3x

Answer 1

Solution :-

→ [2•tan x(sec²x - 1)] / cos³x

using sec² A - 1 = tan² A,

→ [2• tan x • tan²x] / cos³x

→ (2tan³x)/cos³x) ---------- Eqn.(1)

using tan A = sin A / cos A in Eqn.(1)

→ [2•(sin³x/cos³x)] / cos³x

→ (2•sin³x/cos⁶x) (Ans.)

Or, using cos A = 1/sec A in Eqn.(1),

→ (2tan³x) / (1/sec³x)

→ (2•tan³x•sec³x) (Ans.)

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Answer 2

Answer:

2 tan^3x  sec^3x

Step-by-step explanation:

2 tan x (sec^2x-1) /cos^3 x

So, we know that sec^2x−1=tan^2x.

So, that would give you 2 tanx (tan^2 x) / cos^3

Which is nothing but , 2 tan ^3 x / cos^3

Cos^3 x can be written as 1/Sec^3

So when we divide 2 tan^3x by 1/sec^3

We get 2 tan^3 x sec^3 x

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