Advertisements
Advertisements
प्रश्न
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
उत्तर
(sin A + cos A ) sec A
= `( sinA + cos A ) 1/ cos A`
=`(sinA )/( cos A) + ( cos A)/( cos A)`
= tan A + 1
= `5/12 +1/1`
=` (5+12)/12`
=`17/12`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA cosecA + 1`
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
Prove that:
(cosec A – sin A) (sec A – cos A) sec2 A = tan A
`(1 + cot^2 theta ) sin^2 theta =1`
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
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`
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
