Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Advertisements
उत्तर
We know that `sin^2 theta + cos^2 theta = 1`
So
`tan^2 theta cos^2 theta = (tan theta xx cos theta)^2`
`= (sin theta/cos theta xx cos theta)^2`
`= sin^2 theta`
`= 1 - cos^2 theta`
APPEARS IN
संबंधित प्रश्न
`"If "\frac{\cos \alpha }{\cos \beta }=m\text{ and }\frac{\cos \alpha }{\sin \beta }=n " show that " (m^2 + n^2 ) cos^2 β = n^2`
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
If x= a sec `theta + b tan theta and y = a tan theta + b sec theta ,"prove that" (x^2 - y^2 )=(a^2 -b^2)`
If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Prove that cot2θ × sec2θ = cot2θ + 1
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
