Advertisements
Advertisements
Question
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
Advertisements
Solution
`cosec ^2 (90°- theta )- tan^2 theta `
=` sec^2 theta - tan^2 theta`
= 1
APPEARS IN
RELATED QUESTIONS
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 } )`
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Show that : tan 10° tan 15° tan 75° tan 80° = 1
If `sec theta + tan theta = x," find the value of " sec theta`
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
If `1 - cos^2θ = 1/4`, then θ = ?
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3.
Prove that (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B.
If tan α + cot α = 2, then tan20α + cot20α = ______.
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
