Advertisements
Advertisements
Question
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
Advertisements
Solution
L.H.S = `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)`
= `1/("cosec" theta)(cottheta + tantheta)` .....`[(because tan(90 - theta) = cot theta),(cot(90 - theta) = tantheta)]`
= sin θ (cot θ + tan θ)
= `sintheta ((costheta)/(sintheta) + (sintheta)/(costheta))`
= `sintheta ((cos^2theta + sin^2theta)/(sintheta costheta))`
= `sintheta (1/(sintheta costheta))` ......[∵ sin2θ + cos2θ = 1]
= `1/costheta`
= sec θ
= R.H.S
∴ `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
APPEARS IN
RELATED QUESTIONS
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that: `(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(sin^2 A - cos^2 A)`.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
If tan θ = `13/12`, then cot θ = ?
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
