Advertisements
Advertisements
प्रश्न
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
उत्तर १
5`(x^2 - 1/(x^2))`
=`25/5 ( x^2 -1/(x^2))`
=`1/5 (25x^2 - 25/(x^2))`
=`1/5 [ (5x)^2 - (5/x)^2]`
=`1/5 [(sec theta )^2 - ( tan theta )^2 ]`
=`1/5 (sec^2 theta - tan^2 theta)`
=`1/5 (1)`
=`1/5`
उत्तर २
Given:
5x = sec θ, `5/x` = tan θ
⇒ sec θ = 5x, tan θ = `5/x`
We know that,
⇒ `(5x)^2 - (5/x)^2 = 1`
⇒ `25x^2 - 25/x^2 = 1`
⇒ `25 (x^2 - 1/x^2)=1`
⇒ `5 xx 5 xx (x^2 - 1/x^2)=1`
⇒ `5(x^2 - 1/x^2)`
⇒ `1/5`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
(secA + tanA) (1 − sinA) = ______.
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
Show that tan4θ + tan2θ = sec4θ – sec2θ.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
If tan θ = `x/y`, then cos θ is equal to ______.
