Balbharati solutions for Geometry (Mathematics 2) [English] 10 Standard SSC Maharashtra State Board chapter 6 - Trigonometry [Latest edition]

If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tan​θ.

If \[\tan \theta = \frac{3}{4}\], find the values of sec​θ and cos​θ

If \[\cot\theta = \frac{40}{9}\], find the values of cosecθ and sinθ.

If tanθ = 1 then, find the value of

`(sinθ + cosθ)/(secθ + cosecθ)`

Prove that:

`(sin^2θ)/(cosθ) + cosθ = secθ`

Prove that:

cos²θ (1 + tan²θ)

Prove that:

Prove that:

(secθ - cosθ)(cotθ + tanθ) = tanθ.secθ.

Prove that:

Prove that: `1/"sec θ − tan θ" = "sec θ + tan θ"`

Prove that:

Sin⁴θ - cos⁴θ = 1 - 2cos²θ

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:

`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.

Prove that:

Prove that:

`"tanθ"/("secθ"  –  1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`

From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse.

A kite is flying at a height of 60 m above the ground. The string attached to the kite is tied at the ground. It makes an angle of 60° with the ground. Assuming that the string is straight, find the length of the string.

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.

If sinθ = `11/61`, find the values of cosθ using trigonometric identity.

If \[\sec\theta = \frac{13}{12}\], find the values of other trigonometric ratios.

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.

tan⁴θ + tan²θ = sec⁴θ - 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.

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`