Advertisements
Advertisements
प्रश्न
Show that `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) tan(30^circ - theta))` = 1
उत्तर
L.H.S = `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) * tan(30^circ - theta))`
= `(cos^2(45^circ + theta) + [sin{90^circ - (45^circ - theta)}]^2)/(tan(60^circ + theta) * cot{90^circ - (30^circ - theta)})` ...[∵ sin(90° – θ) = cos θ and cot(90° – θ) = tan θ]
= `(cos^2(45^circ + theta) + sin^2(45^circ + theta))/(tan(60^circ + theta) * cot(60^circ + theta))` ...[∵ sin2θ + cos2θ = 1]
= `1/(tan(60^circ + theta) * 1/(tan(60^circ + theta))` ...`[∵ cot θ = 1/tanθ]`
= 1
= R.H.S
APPEARS IN
संबंधित प्रश्न
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
`(1 + cot^2 theta ) sin^2 theta =1`
` tan^2 theta - 1/( cos^2 theta )=-1`
`1/((1+ sintheta ))+1/((1- sin theta ))= 2 sec^2 theta`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`tan^2A - sin^2A = tan^2A.sin^2A`
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
