Advertisements
Advertisements
प्रश्न
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
उत्तर
L.H.S. = x2 + y2 + z2
= (r cos A cos B)2 + (r cos A sin B)2 + (r sin A)2
= r2 cos2 A cos2 B + r2 cos2 A sin2 B + r2 sin2 A
= r2 cos2 A (cos2 B + sin2 B) + r2 sin2 A
= r2 (cos2 A + sin2 A)
= r2 = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
If cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
Prove that `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A
Prove that
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`
Show that tan4θ + tan2θ = sec4θ – sec2θ.
