Prove that √1+tan^2x /√1-sin^2=sec^2x?

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Prove that √1+tan^2x /√1-sin^2=sec^2x?

Prove that, $sqrt(1+tan^2x)/sqrt(1-sin^2x)=sec^2x.$

2 Answers

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Answer 1 · 2018-05-10T16:43:08

Please see below.

Explanation:

We know that,

$color(red)((1)1+tan^2theta=sec^2theta$

$color(blue)((2)1-sin^2theta=cos^2theta$

$color(violet)((3)costheta=1/sectheta$

Here,

$sqrt(1+tan^2x)/sqrt(1-sin^2x)=sec^2x$

Let,

$LHS=sqrt(1+tan^2x)/sqrt(1-sin^2x)$

Using $(1) and (2)$ we get

$LHS=sqrt(color(red)(sec^2x))/sqrt(color(blue)(cos^2x))$

$color(white)(LHS)=secx/color(violet)(cosx$

$color(white)(LHS)=secx/color(violet)((1/secx)$

$color(white)(LHS)=secx*secx$

$color(white)(LHS)=sec^2x$

$:.LHS=RHS$

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Answer 2 · 2018-05-10T19:35:12

$"see explanation"$

Explanation:

$"using the "color(blue)"trigonometric identities"$

$•color(white)(x)1+tan^2x=sec^2x$

$rArrsqrt(1+tan^2x)=secx$

$•color(white)(x)sin^2x+cos^2x=1$

$rArrsqrt(1-sin^2x)=cosx$

$"consider the left side"$

$rArrsqrt(1+tan^2x)/sqrt(1-sin^2x)$

$=secx/cosx$

$=1/cosx xx1/cosx$

$=1/cos^2x=sec^2x=" right side "rArr"verified"$

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Prove that √1+tan^2x /√1-sin^2=sec^2x?

Prove that, $sqrt(1+tan^2x)/sqrt(1-sin^2x)=sec^2x.$

2 Answers

Explanation:

Explanation:

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Prove that √1+tan^2x /√1-sin^2=sec^2x?

Prove that, sqrt(1+tan^2x)/sqrt(1-sin^2x)=sec^2x.sqrt(1+tan^2x)/sqrt(1-sin^2x)=sec^2x.

2 Answers

Explanation:

Explanation:

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Prove that, $sqrt(1+tan^2x)/sqrt(1-sin^2x)=sec^2x.$