Advertisements
Advertisements
प्रश्न
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
Advertisements
उत्तर
` (( cosec^2 theta - sec^2 theta))/((cosec^2 theta + sec^2 theta))`
=` ((1+cot^2 theta) -( 1+ tan^2 theta))/((1+ cot^2 theta)+( 1+ tan^2 theta))`
=`((1+ 1/ tan^2 theta)-(1+ tan^2 theta))/((1+ 1/ tan^2 theta)-(1+ tan^2 theta))`
=`((1+ 1/ tan^2 theta-1- tan^2 theta))/((1+ 1/ tan^2 theta +1+ tan^2 theta))`
=` ((1/ tan^2 theta - tan^2 theta ))/((1/ tan^2 theta + tan^2 theta +2))`
=`((sqrt(5)/1)^2 - ( 1/sqrt(5))^2 )/((sqrt(5)/1)^2 + (1/sqrt(5))^2+2)`
=`((5/1+1/5))/((5/1+1/5+2/1))`
=`((24/5))/((36/5))`
=`24/36`
=`2/3`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`
`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`
`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following trigonometric identities.
sec6θ = tan6θ + 3 tan2θ sec2θ + 1
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
Write the value of tan1° tan 2° ........ tan 89° .
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
(sec A + tan A) (1 − sin A) = ______.
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Prove that `(cos(90 - "A"))/(sin "A") = (sin(90 - "A"))/(cos "A")`
If cos θ = `24/25`, then sin θ = ?
