Advertisements
Advertisements
प्रश्न
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
Advertisements
उत्तर
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`
cosec2θ − sec2θ − cot2θ − tan2θ − cos2θ − sin2θ = −3 ...`[because sintheta = 1/(cosectheta), costheta = 1/(sectheta), tantheta = 1/(cottheta)]`
⇒ 1 + cot2θ − 1 − tan2θ − cot2θ − tan2θ − 1 = −3
⇒ − 2 tan2θ − 1 = − 3 ...`[(because 1 + cot^2theta = cosec^2theta), (1 + sec^2theta = tan^2theta), (sin^2theta + cos^2theta = 1)]`
⇒ −2 tan2θ = − 3 + 1
⇒ −2 tan2θ = −2
⇒ tan2θ = 1
⇒ tan θ = 1 ...(Taking square root on both sides)
⇒ tan θ = tan 45°
∴ θ = 45°
APPEARS IN
संबंधित प्रश्न
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta )/(cos theta)`
Prove the following identities:
`(cot^2 theta (sec theta - 1))/((1 + sin theta)) + (sec^2 theta(sin theta - 1))/((1 + sec theta)) = 0`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
If `sec theta + tan theta = x," find the value of " sec theta`
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
If tan α = n tan β, sin α = m sin β, prove that cos2 α = `(m^2 - 1)/(n^2 - 1)`.
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
`sin θ = 1/2`, then θ = ?
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0.
