SSC (English Medium) 10th Standard - Maharashtra State Board Question Bank Solutions

Prove that:

Prove that:
If \[\tan\theta + \frac{1}{\tan\theta} = 2\], then show that \[\tan^2 \theta + \frac{1}{\tan^2 \theta} = 2\]

Prove that:

Choose the correct alternative answer for the following question.
sin \[\theta\] cosec \[\theta\]= ?

Choose the correct alternative answer for the following question.
cosec 45^° =?

Choose the correct alternative answer for the following question.

1 + tan² \[\theta\]  = ?

Choose the correct alternative answer for the following question.

Prove the following.

secθ (1 – sinθ) (secθ + tanθ) = 1

Prove the following.
(secθ + tanθ) (1 – sinθ) = cosθ

Prove the following.
sec²θ + cosec²θ = sec²θ × cosec²θ 

Prove the following.
cot²θ – tan²θ = cosec²θ – sec²θ

Prove the following.

Prove the following:

sec⁶x – tan⁶x = 1 + 3sec²x × tan²x

Prove the following.

\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]

Prove the following.

In the adjoining figure, point O is the centre of the cirlcle, seg OM ⊥ chord AB. If OM = 8cm, AB = 12 cm, then find OB.

In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?

Sides of the triangle are 7 cm, 24 cm, and 25 cm. Determine whether the triangle is a right-angled triangle or not. 

Choose the correct alternative: 
sinθ × cosecθ =?