Advertisements
Advertisements
प्रश्न
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 .
Advertisements
उत्तर
\[\sin\theta = x + \frac{1}{x}\]
\[ \Rightarrow - 1 \leq x + \frac{1}{x} \leq 1\]
\[ \Rightarrow x + \frac{1}{x} \leq 1\]
\[ \Rightarrow x^2 + 1 \leq x\]
\[ \Rightarrow x^2 + 1 - x \leq 0\]
\[\text{ Take } x = 1, \]
\[ \Rightarrow 1 + 1 - 1 \leq 0\]
\[ \Rightarrow 1 \leq 0\]
\[\text{ Which is false, so x is not always a positive real number . \]
\[The given statement is false } .\]
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
cos4 A − sin4 A is equal to ______.
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
(sec A + tan A) (1 − sin A) = ______.
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If tan θ = `x/y`, then cos θ is equal to ______.
