Advertisements
Advertisements
प्रश्न
Prove the following.
sec2θ + cosec2θ = sec2θ × cosec2θ
Advertisements
उत्तर
\[ = \frac{1}{\cos^2 \theta} + \frac{1}{\sin^2 \theta}\]
\[ = \frac{\sin^2 \theta + \cos^2 \theta}{\cos^2 \theta \sin^2 \theta}\]
\[ = \frac{1}{\cos^2 \theta \sin^2 \theta}\]
\[ = \frac{1}{\cos^2 \theta} \times \frac{1}{\sin^2 \theta}\]
\[ = \sec^2 \theta \text{ cosec }^2 \theta\]
APPEARS IN
संबंधित प्रश्न
If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tanθ.
If \[\tan \theta = \frac{3}{4}\], find the values of secθ and cosθ
If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ, and sinθ.
Prove that:
cos2θ (1 + tan2θ)
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° =?
Prove the following.
secθ (1 – sinθ) (secθ + tanθ) = 1
Prove the following.
cot2θ – tan2θ = cosec2θ – sec2θ
Prove the following.
Prove the following.
\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]
Prove the following.
If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.
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.
