Advertisements
Advertisements
प्रश्न
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
Advertisements
उत्तर
L.H.S. = `(cot A)/(1 - cot A) + (tan A)/(1 - tan A)`
= `(cot A)/(1 - 1/(tan A)) + (tan A)/(1 - tan A)`
= `(cot A)/((tan A - 1)/(tan A)) + (tan A)/(1 - tan A)`
= `(cot A tan A)/(tan A - 1) + (tan A)/(1 - tan A)`
= `1/(tan A - 1) + (tan A)/(1 - tan A)` ...[∵ cot A tan A = 1]
= `- 1/(1 - tan A) + (tan A)/(1 - tan A)`
= `- (1/(1 - tan A) - (tan A)/(1 - tan A))`
= `-((1 - tan A)/(1 - tan A))`
= –1
= R.H.S.
∴ `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`
APPEARS IN
संबंधित प्रश्न
Evaluate sin25° cos65° + cos25° sin65°
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
(sec A + tan A) (1 − sin A) = ______.
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Prove that:
tan (55° + x) = cot (35° – x)
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
If 3 sin θ = 4 cos θ, then sec θ = ?
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
