Advertisements
Advertisements
प्रश्न
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
विकल्प
9
7
5
3
Advertisements
उत्तर
7
Explanation;
(sin α + cos α)2 + (cos α + sec α)2
= sin2α + cosec2α + 2 sin α cosec α + cos2α + sec2α + 2 cos α sec α
= 1 + cosec2α + 2 + sec2α + 2
= 1 + cot2α + 1 + 2 + tan2α + 1 + 2
= 7 + tan2α + cot2α
k = 7
APPEARS IN
संबंधित प्रश्न
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If `tan θ = 9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ...[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
Show that tan4θ + tan2θ = sec4θ – sec2θ.
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
