Advertisements
Advertisements
प्रश्न
Prove that:
Advertisements
उत्तर
\[\sqrt{\frac{1 - \sin\theta}{1 + \sin\theta}}\]
\[ = \sqrt{\frac{1 - \sin\theta}{1 + \sin\theta} \times \frac{1 - \sin\theta}{1 - \sin\theta}}\]
\[ = \sqrt{\frac{\left( 1 - \sin\theta \right)^2}{1 - \sin^2 \theta}}\]
\[ = \sqrt{\frac{\left( 1 - \sin\theta \right)^2}{\cos^2 \theta}} \left( \cos^2 \theta + \sin^2 \theta = 1 \right)\]
\[= \frac{1 - \sin\theta}{\cos\theta}\]
\[ = \frac{1}{\cos\theta} - \frac{\sin\theta}{\cos\theta}\]
\[ = \sec\theta - \tan\theta\]
APPEARS IN
संबंधित प्रश्न
If \[\cot\theta = \frac{40}{9}\], find the values of cosecθ and sinθ.
If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ, and sinθ.
If tanθ = 1 then, find the value of
`(sinθ + cosθ)/(secθ + cosecθ)`
Prove that:
cos2θ (1 + tan2θ)
Prove that:
(secθ - cosθ)(cotθ + tanθ) = tanθ.secθ.
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.
cosec 45° =?
Choose the correct alternative answer for the following question.
1 + tan2 \[\theta\] = ?
Prove the following.
sec2θ + cosec2θ = sec2θ × cosec2θ
Prove the following:
sec6x – tan6x = 1 + 3sec2x × tan2x
Choose the correct alternative:
sinθ × cosecθ =?
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"`
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.
