Advertisements
Advertisements
प्रश्न
If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`
Advertisements
उत्तर
We have ,
`cot theta = 1/ sqrt(3)`
⇒` cot theta = cot (π/3)`
⇒`theta = π/3`
Now ,
`((1- cos^2 theta))/((2 - sin^2 theta))`
= `(1- cos ^2(π/3))/( 2 - sin ^2 ( π/ 3))`
=` (1- (1/2)^2)/(2-(sqrt(3)/2)^2)`
=` ((1/1 - 1/4))/((2/1-3/4))`
=`((3/4))/((5/4))`
=`3/5`
APPEARS IN
संबंधित प्रश्न
(secA + tanA) (1 − sinA) = ______.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
If \[\cos A = \frac{7}{25}\] find the value of tan A + cot A.
Write True' or False' and justify your answer the following :
The value of \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x' is a positive real number .
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Choose the correct alternative:
sec2θ – tan2θ =?
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 ______.
