Advertisements
Advertisements
प्रश्न
If tanθ = 1 then, find the value of
`(sinθ + cosθ)/(secθ + cosecθ)`
Advertisements
उत्तर
tanθ = 1 ...(Given)
We know that, tan45° = 1
∴ θ = 45º
Now,
sinθ = sin 45º = `1/sqrt2`
cosθ = cos 45º = `1/sqrt2`
secθ = sec 45º = `sqrt2`
cosecθ = cosec 45º = `sqrt2`
∴ `(sinθ + cosθ)/(secθ + cosecθ)`
⇒ `(1/sqrt2 + 1/sqrt2)/(sqrt2 + sqrt2)`
⇒ `(2/sqrt2)/(2sqrt2)`
⇒ `cancel2/sqrt2 × 1/(cancel2sqrt2)`
⇒ `1/2`
∴ `(sinθ + cosθ)/(secθ + cosecθ) = 1/2`
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: `1/"sec θ − tan θ" = "sec θ + tan θ"`
Prove that:
Prove that:
If \[\tan\theta + \frac{1}{\tan\theta} = 2\], then show that \[\tan^2 \theta + \frac{1}{\tan^2 \theta} = 2\]
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 + tanθ) (1 – sinθ) = cosθ
Prove the following.
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"`
