Advertisements
Advertisements
प्रश्न
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
Advertisements
उत्तर
L.H.S. = \[\boxed{\text{cos}^2θ · (1 + \text{tan}^2θ)}\]
= cos2θ × \[\boxed{\text{sec}^2θ}\] ...[1 + tan2θ = \[\boxed{\text{sec}^2θ}\]]
= (cos θ × \[\boxed{\text{sec} θ}\])2
= 12
= 1
= R.H.S.
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`
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
If `cot theta = 1/ sqrt(3)`, write the value of `((1 - cos^2 theta))/((2 - sin^2 theta))`.
Write the value of tan10° tan 20° tan 70° tan 80° .
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Find the value of ( sin2 33° + sin2 57°).
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
If `sin θ + cos θ = sqrt(3)`, then show that tan θ + cot θ = 1.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
