Advertisements
Advertisements
Question
Choose the correct alternative:
`(1 + cot^2"A")/(1 + tan^2"A")` = ?
Options
tan2A
sec2A
cosec2A
cot2A
Advertisements
Solution
cot2A
`(1 + cot^2"A")/(1 + tan^2"A")`
= `("cosec"^2"A")/("sec"^2"A")`
= `(1/("sin"^2"A"))/(1/("cos"^2"A"))`
= `("cos"^2"A")/("sin"^2"A")`
= cot2A
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
(i)` (1-cos^2 theta )cosec^2theta = 1`
`(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:
`tan^2 theta + sin theta = cos^2 theta`
Write the value of tan1° tan 2° ........ tan 89° .
What is the value of 9cot2 θ − 9cosec2 θ?
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Write True' or False' and justify your answer the following :
The value of \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x' is a positive real number .
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Evaluate:
`(tan 65^circ)/(cot 25^circ)`
Prove that `sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A - 1) = 1`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove that `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)
sin(45° + θ) – cos(45° – θ) is equal to ______.
If tan θ = `x/y`, then cos θ is equal to ______.
