Question

⚪⚪Hello Mates⚪⚪

⚡Answer the question.⚡

❄ ATTACHMENT❄

Answer 1

Answer:

$\huge\boxed{\boxed{\red{OPTION\:C}}}$

Step-by-step explanation:

tan² Ф = 1 - e²

Add 1 to both sides :

⇒ 1 + tan²Ф = 1 + 1 - e²

⇒ 1 + tan²Ф = 2 - e²

We know that 1 + tan²Ф = sec²Ф

⇒ sec²Ф = 2 - e²

We have to find the value of sec Ф + tan³Ф × cosec Ф

sec Ф = 1/cos Ф

tan Ф = sin Ф / cos Ф

cosec Ф = 1 / sin Ф

So inserting these values we will get :

⇒ 1/cos Ф + ( sin³Ф/cos³Ф ) × 1/sin Ф

⇒ 1/cos Ф + ( sin²Ф / cos³Ф )

⇒ ( cos²Ф + sin²Ф ) / ( cos³Ф )

Take cos²Ф + sin²Ф as 1 :

⇒ 1/cos³Ф

⇒ sec³Ф

We note that sec²Ф was 2 - e²

Take the root of $\frac{3}{2}$ both sides :

$\implies (sec^2\theta)^{3/2}=((2-e^2))^{3/2}\\\\\implies sec^3\theta=(2-e^2)^{3/2}$

Hence the answer is OPTION C.

Answer 2

$\boxed{Explained\:Answer}$

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