Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
sec2θ = 1 + \[\boxed{\text{tan}^2θ}\] ...[Fundamental trigonometric identity]
∴ sec2θ = 1 + \[\boxed{\frac{9}{40}}^2\]
∴ sec2θ = 1 + \[\boxed{\frac{81}{1600}}\]
∴ sec2θ = `1681/1600`
∴ sec θ = \[\boxed{\frac{41}{40}}\]
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
The value of sin2 29° + sin2 61° is
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
cos 45° = ?
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
