Advertisements
Advertisements
Question
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Advertisements
Solution
It is given that A = 60°, B = 30°
Putting A = 60° and B = 30° in the given equation,
we get
tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`
⇒ tan( 60° - 30° ) = `(tan 60° - tan 30° )/(1 + tan 60°. tan 30° )`
⇒ tan 30° = `(sqrt3 - 1/sqrt3)/(1 + sqrt3 xx 1/sqrt3)`
⇒ `((3-1)/sqrt3)/2`
⇒ `(2/sqrt3)/(2/1)`
⇒ `2/(2sqrt3)`
⇒ `1/sqrt3`
⇒ LHS = RHS
RELATED QUESTIONS
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
What is the value of (1 − cos2 θ) cosec2 θ?
If sec θ = `25/7`, then find the value of tan θ.
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
