Advertisements
Advertisements
Question
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
Advertisements
Solution
R.H.S `m^2 sin^2 theta`
`= (a cos theta + b sin theta)^2 + (a sin theta - b cos theta)^2`
`= a^2 cos^2 theta + b^2 sin^2 theta + 2 ab sin theta cos theta + a^2 sin^2 theta + b^2 cos^2 theta - 2 ab sin theta cos theta`
`= a^2 cos^2 theta + b^2 cos^2 theta + b^2 sin^2 theta + a^2 sin^2 theta`
`= a^2(sin^2 theta + cos^2 theta) + b^2(sin^2 theta + cos^2 theta)`
`=a^2 + b^2` (∵ `sin^2 theta + cos^2 theta = 1`)
APPEARS IN
RELATED QUESTIONS
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
Prove that
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
