Advertisements
Advertisements
प्रश्न
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
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
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
`(sec^2 theta-1) cot ^2 theta=1`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
If `sec theta = x ,"write the value of tan" theta`.
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Evaluate:
`(tan 65°)/(cot 25°)`
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`