Advertisements
Advertisements
Question
Show that `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) tan(30^circ - theta))` = 1
Solution
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
RELATED QUESTIONS
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
