What is the Value of (1 − Cos2 θ) Cosec2 θ? - Mathematics

Question

What is the value of (1 − cos² θ) cosec² θ?

Answer in Brief

Solution

We have,

$(1 - \cos^{2} θ) \cos e c^{2} θ = \sin^{2} θ \times \cos e c^{2} θ$

= $\sin^{2} θ \times {(\frac{1}{\sin θ})}^{2}$

= $\sin^{2} θ \times \frac{1}{\sin^{2} θ}$

$= 1$

shaalaa.com

Trigonometric Identities

Is there an error in this question or solution?

Q 2 Q 1 Q 3

Chapter 11: Trigonometric Identities - Exercise 11.3 [Page 55]

APPEARS IN

RD Sharma Mathematics [English] Class 10

Chapter 11 Trigonometric Identities
Exercise 11.3 | Q 2 | Page 55

Video TutorialsVIEW ALL [6]

RELATED QUESTIONS

Prove the following identities:

$(i) {\cos 4}^{4} A - \cos^{2} A = \sin^{4} A - \sin^{2} A$

$(i i) \cot^{4} A - 1 = \cos e c^{4} A - 2 \cos e c^{2} A$

$(i i i) \sin^{6} A + \cos^{6} A = 1 - 3 \sin^{2} A \cos^{2} A .$

Prove the following trigonometric identities.

tan²θ cos²θ = 1 − cos²θ

If cos θ + cos² θ = 1, prove that sin¹² θ + 3 sin¹⁰ θ + 3 sin⁸ θ + sin⁶ θ + 2 sin⁴ θ + 2 sin² θ − 2 = 1

Prove the following identities:

cosec⁴A – cosec² A = cot⁴ A + cot² A

Prove the following identities:

$\frac{\sin A \tan A}{1 - \cos A} = 1 + \sec A$

$\cot^{2} θ - \frac{1}{\sin^{2} θ} = - 1$ a

If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.

If $\sin θ = \frac{1}{3}$ then find the value of 9tan² θ + 9.

Prove the following identity :

$\tan^{2} A - \sin^{2} A = \tan^{2} A . \sin^{2} A$

Prove the following identity :

$\frac{\cos e c A}{\cos e c A - 1} + \frac{\cos e c A}{\cos e c A + 1} = 2 \sec^{2} A$

Prove the following identity :

$2 (\sin^{6} θ + \cos^{6} θ) - 3 (\sin^{4} θ + \cos^{4} θ) + 1 = 0$

Prove that $\frac{\sin θ \tan θ}{1 - \cos θ} = 1 + \sec θ .$

Without using trigonometric table, prove that
$\cos^{2} 26 ° + \cos 64 ° \sin 26 ° + \frac{\tan 36 °}{\cot 54 °} = 2$

If sin θ + cos θ = $\sqrt{3}$ , then prove that tan θ + cot θ = 1

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = $\pm \sqrt{a^{2} + b^{2} - c^{2}}$

If tan θ = $\frac{9}{40}$ , complete the activity to find the value of sec θ.

Activity:

sec²θ = 1 + $□$ ......[Fundamental trigonometric identity]

sec²θ = 1 + $□^{2}$

sec²θ = 1 + $□$

sec θ = $□$

Prove that sec²θ + cosec²θ = sec²θ × cosec²θ

If sin θ + cos θ = $\sqrt{3}$ , then show that tan θ + cot θ = 1

tan θ × $\sqrt{1 - \sin^{2} θ}$ is equal to:

What is the Value of (1 − Cos2 θ) Cosec2 θ? - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [6]

RELATED QUESTIONS

Select a course

What is the Value of (1 − Cos2 θ) Cosec2 θ? - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [6]

RELATED QUESTIONS

Select a course

Solution