Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Advertisements
उत्तर
We have to prove `cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
We know that `sin^2 theta + cos^2 theta = 1`
So,
`cot theta - tan theta = (cos theta)/(sin theta) - (sin theta)/(cos theta)`
`= (cos^2 theta - sin^2 theta)/(sin theta cos theta)`
`= (cos^2 theta - (1 - cos^2 theta))/(sin theta cos theta)`
`= (cos^2 theta - 1 + cos^2 theta)/(sin theta cos theta)`
`= (2 cos^2 theta - 1)/(sin theta cos theta)`
APPEARS IN
संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Show that : tan 10° tan 15° tan 75° tan 80° = 1
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos (α - β)/2` is ______.
