Advertisements
Advertisements
प्रश्न
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
Advertisements
उत्तर
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
L.H.S = [(sin θ + sec θ)2 + (cos θ + cosec θ)2]
= [sin2 θ + sec2 θ + 2 sin θ sec θ + cos2 θ + cosec2 θ + 2 cos θ cosec θ]
= (sin2θ + cos2θ) + (sec2θ + cosec2θ) + 2 (sinθ secθ + cos θ cosec θ)
= `1 + sec^2 theta + "cosec"^2 theta + 2[sin theta xx 1/cos theta + cos theta xx 1/sin theta]`
= `1 + sec^2 theta + "cosec"^2 theta + 2 [(sin^2 theta + cos^2 theta)/(sintheta cos theta)]`
= `1 + sec^2 theta + "cosec"^2 theta + 2 xx 1/(sintheta costheta)`
= 1 + sec2θ + cosec2θ + 2 secθ cosecθ
= 1 + (secθ + cosecθ)2
L.H.S = R.H.S
∴ (sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S = `square`
= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
= R.H.S
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
If cosA + cos2A = 1, then sin2A + sin4A = 1.
