SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Important Questions for Geometry Mathematics 2

Choose the correct alternative:

1 + tan² θ = ?

If sec θ = `25/7`, then find the value of tan θ.

The terminal is in II (second ) quadrant. what is the possible measure of an angle?

If tan θ = 2, where θ is an acute angle, find the value of cos θ. 

Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A. 

If sin θ = `1/2`, then find the value of θ. 

Choose the correct alternative: 
sinθ × cosecθ =?

If cosθ = `5/13`, then find sinθ. 

Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle. 

For the angle in standard position if the initial arm rotates 305° in an anticlockwise direction, then state the quadrant in which the terminal arm lies.

Find the trigonometric sine ratio of an angle in a standard position whose terminal arm passes through the point (3, 4).

If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.

Show that: 

`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`

In ΔPQR, ∠P = 30°, ∠Q = 60°, ∠R = 90° and PQ = 12 cm, then find PR and QR.

ΔAMT∼ΔAHE, construct Δ AMT such that MA = 6.3 cm, ∠MAT=120°, AT = 4.9 cm and `"MA"/"HA"=7/5`, then construct ΔAHE.

If sec θ = `25/7`, find the value of tan θ.

Solution:

1 + tan² θ = sec² θ

∴ 1 + tan² θ = `(25/7)^square`

∴ tan² θ = `625/49 - square`

= `(625 - 49)/49`

= `square/49`

∴ tan θ = `square/7` ........(by taking square roots)

If sin θ + sin² θ = 1 show that: cos² θ + cos⁴ θ = 1

sin²θ + sin²(90 – θ) = ?

`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?

If tan θ = `9/40`, complete the activity to find the value of sec θ.

Activity:

sec²θ = 1 + `square`     ......[Fundamental trigonometric identity]

sec²θ = 1 + `square^2`

sec²θ = 1 + `square` 

sec θ = `square`