Advertisements
Advertisements
प्रश्न
Show that none of the following is an identity:
`cos^2theta + cos theta = 1`
Advertisements
उत्तर
`cos^2theta + cos theta =1`
LHS = `cos^2 theta + cos theta`
=`1- sin^2 theta + cos theta `
=` 1- ( sin^2 theta - cos theta )`
Since LHS ≠ RHS, this not an identity.
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following trigonometric identities:
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
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 that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
Write the value of cosec2 (90° − θ) − tan2 θ.
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
