Advertisements
Advertisements
प्रश्न
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
Advertisements
उत्तर
Given:` secθ+tanθ=x`
We know that,
`Sec^2θ-tan^2θ=1`
Therefore,
`sec^2 θ-tan^2θ=1`
⇒` (Secθ+tan θ) (Secθ-tan θ)=1`
⇒` x (secθ-tan θ )=1`
⇒ `(sec θ-tan θ)=1/x`
Hence, `sec θ-tan θ=1/4`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove the following identity :
secA(1 - sinA)(secA + tanA) = 1
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Prove that `sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A - 1) = 1`.
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3
If tan θ – sin2θ = cos2θ, then show that sin2 θ = `1/2`.
Given that sin θ = `a/b`, then cos θ is equal to ______.
