Advertisements
Advertisements
प्रश्न
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
उत्तर
L.H.S. = (sin θ + cos θ)(tan θ + cot θ)
= `(sin theta + cos theta)(sin theta/cos theta + costheta/sin theta)`
= `(sin theta + cos theta)((sin^2 theta + cos^2 theta)/(costhetasin theta))`
= `(sintheta+costheta)xx1/(sinthetacostheta)` ...[∵ sin2θ + cos2θ = 1]
= `(sin theta + cos theta)/(cos theta sin theta)`
= `sin theta/(cos thetasin theta) + cos theta/(cos theta sin theta)`
= `1/cos theta + 1/sin theta`
= `sec theta + cosec theta`
= R.H.S
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following trigonometric identities.
sec6θ = tan6θ + 3 tan2θ sec2θ + 1
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
`(sec^2 theta-1) cot ^2 theta=1`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then
(sec A + tan A) (1 − sin A) = ______.
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt("a"^2 + "b"^2 -"c"^2)`
If 2sin2β − cos2β = 2, then β is ______.
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
If cosA + cos2A = 1, then sin2A + sin4A = 1.
Show that `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) tan(30^circ - theta))` = 1
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
(1 + sin A)(1 – sin A) is equal to ______.
