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
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
