Advertisements
Advertisements
Question
Verify the following equalities:
1 + tan2 30° = sec2 30°
Solution
tan 30° = `1/sqrt(3)`, sec 30° = `2/sqrt(3)`
L.H.S = 1 + tan2 30°
= `1 + (1/sqrt(3))^2`
= `1 + (1/3)`
= `((3 + 1)/3)`
= `4/3`
R.H.S = sec2 30°
= `(2/sqrt(3))^2`
= `4/3`
∴ L.H.S = R.H.S
Hence it is proved.
APPEARS IN
RELATED QUESTIONS
Show that:
(i) `2(cos^2 45º + tan^2 60º) – 6(sin^2 45º – tan^2 30º) = 6`
(ii) `2(cos^4 60º + sin^4 30º) – (tan^2 60º + cot^2 45º) + 3 sec^2 30º = 1/4`
Express cos 75° + cot 75° in terms of angles between 0° and 30°.
Evaluate: `cos 58^@/sin 32^@ + sin 22^@/cos 68^@ - (cos 38^@ cosec 52^@)/(tan 18^@ tan 35^@ tan 60^@ tan 72^@ tan 65^@)`
If `sqrt3` = 1.732, find (correct to two decimal place) the value of sin 60o
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Without using tables, find the value of the following: `(tan45°)/("cosec"30°) + (sec60°)/(cot45°) - (5sin90°)/(2cos0°)`
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.
Find the value of 8 sin 2x, cos 4x, sin 6x, when x = 15°
