R d sharma solutions mathematics class 10 Solutions for Chapter 4 trigonometric ratios

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

sin θ = 11/15

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

cos A = 4/5

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

sin A = 2/3

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

tan θ = 11/1

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

tan α = 5/12

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

sin θ = √3/2

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

tan θ = 8/15

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

cot θ = 12/5

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

sec θ = 13/5

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

cosec θ = √10

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

cos θ =12/15

In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.

cos θ = 7/25

Prove that:

tan 20° tan 35° tan 45° tan 55° tan 70° = 1

Prove that:

sin 48° sec 48° + cos 48° cosec 42° = 2

Prove that:

\frac{\sin 70^{\circ}}{\cos 20^{\circ}}+\frac{\operatorname{cosec} 20^{\circ}}{\sec 70^{\circ}}-2 \cos 70^{\circ} \quad \operatorname{cosec} 42^{\circ}=0

Prove that:

\frac{\cos 80^{\circ}}{\sin 10^{\circ}}+\cos 59^{\circ} \operatorname{cosec} 31^{\circ}=2

Prove the following:

sinθ sin (90^o – θ) – cos θ cos (90^o – θ) = 0

Prove the following:

\frac{\cos \left(90^{\circ}-\theta\right) \sec \left(90^{\circ}-\theta\right) \tan \theta}{\operatorname{cosec}\left(90^{\circ}-\theta\right) \sin \left(90^{\circ}-\theta\right) \cot \left(90^{\circ}-\theta\right)}+\frac{\tan \left(90^{\circ}-\theta\right)}{\cot \theta}=2

Prove the following:

\frac{\tan \left(90^{\circ}-\mathrm{A}\right) \cot \mathrm{A}}{\operatorname{cosec}^{2} \mathrm{~A}}-\cos ^{2} \mathrm{~A}=0

Prove the following:

\frac{\cos \left(90^{\circ}-\mathrm{A}\right) \sin \left(90^{\circ}-\mathrm{A}\right)}{\tan \left(90^{\circ}-\mathrm{A}\right)}=\sin ^{2} \mathrm{~A}

Prove the following:

sin (50^o + θ) – cos (40^o – θ) + tan 1^o tan 10^o tan 20^o tan 70^o tan 80^o tan 89^o = 1