Advertisements
Advertisements
Question
If A =30o, then prove that :
cos 2A = cos2A - sin2A = `(1 – tan^2"A")/(1+ tan^2"A")`
Solution
Given A = 30°
cos2A = cos 2 (30°) = cos 60° = `(1)/(2)`
= `(3)/(4) – (1)/(4)`
= `(1)/(2)`
`(1 – tan^2"A")/(1 + tan^2"A") = (1 – tan^2 30°)/(1 + tan^2 30°)`
= `(1 – (1)/(3))/(1+(1)/(3)`
= `(2)/(4)`
= '(1)/(2)`
∴ cos 2A = `cos^"A" – sin^2"A" = (1 – tan^2"A")/(1 + tan^2"A")`
APPEARS IN
RELATED QUESTIONS
Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º
Evaluate the following:
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
State whether the following is true or false. Justify your answer.
The value of cos θ increases as θ increases.
Evaluate the following :
`cos 19^@/sin 71^@`
Evaluate the following :
`(sin 21^@)/(cos 69^@)`
Evaluate the following :
`(cot 40^@)/cos 35^@ - 1/2 [(cos 35^@)/(sin 55^@)]`
Evaluate the following
sec 50º sin 40° + cos 40º cosec 50º
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
tan 65° + cot 49°
Evaluate: tan 7° tan 23° tan 60° tan 67° tan 83°
Evaluate: `cos 58^@/sin 32^@ + sin 22^@/cos 68^@ - (cos 38^@ cosec 52^@)/(tan 18^@ tan 35^@ tan 60^@ tan 72^@ tan 65^@)`
Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.
sin67° + cos75°
find the value of: cosec2 60° - tan2 30°
Given A = 60° and B = 30°,
prove that: tan (A - B) = `(tan"A" – tan"B")/(1 + tan"A".tan"B")`
Without using tables, evaluate the following: sin60° sin30°+ cos30° cos60°
Without using tables, find the value of the following: `(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`
Without using tables, find the value of the following: `(4)/(cot^2 30°) + (1)/(sin^2 60°) - cos^2 45°`
Prove that : cos60° . cos30° - sin60° . sin30° = 0
Find the value of x in the following: 2 sin3x = `sqrt(3)`
If A = 30° and B = 60°, verify that: sin (A + B) = sin A cos B + cos A sin B
If A = 30° and B = 60°, verify that: `(sin("A" -"B"))/(sin"A" . sin"B")` = cotB - cotA
If A = B = 45°, verify that cos (A − B) = cos A. cos B + sin A. sin B
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
If tan `"A" = (1)/(2), tan "B" = (1)/(3) and tan("A" + "B") = (tan"A" + tan"B")/(1 - tan"A" tan"B")`, find A + B.
Verify the following equalities:
sin 30° cos 60° + cos 30° sin 60° = sin 90°
If sin 30° = x and cos 60° = y, then x2 + y2 is
The value of cos1°. cos2°. cos3°. cos4°....................... cos90° is ______.
The value of 5 sin2 90° – 2 cos2 0° is ______.
Evaluate: `(5 "cosec"^2 30^circ - cos 90^circ)/(4 tan^2 60^circ)`
Find the value of x if `2 "cosec"^2 30 + x sin^2 60 - 3/4 tan^2 30` = 10
