Advertisements
Advertisements
Question
If tan θ = cot θ and 0°∠θ ∠90°, state the value of θ
Solution
tan θ = cotθ
tan θ = `(1)/(tanθ )`
tan2 θ = 1
tan θ = 1
tan θ = tan 45°
θ = 45°
APPEARS IN
RELATED QUESTIONS
Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º
If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3`; 0° < A + B ≤ 90°; A > B, find A and B.
Evaluate the following:
`(cos 45°)/(sec 30° + cosec 30°)`
`(1- tan^2 45°)/(1+tan^2 45°)` = ______
State whether the following are true or false. Justify your answer.
cot A is not defined for A = 0°.
Show that tan 48° tan 23° tan 42° tan 67° = 1
Evaluate the following :
`tan 10^@/cot 80^@`
Evaluate the following :
`tan 35^@/cot 55^@ + cot 78^@/tan 12^@ -1`
Prove that `cos 80^@/sin 10^@ + cos 59^@ cosec 31^@ = 2`
Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`
find the value of: sin2 30° + cos2 30°+ cot2 45°
find the value of: cos2 60° + sec2 30° + tan2 45°
find the value of :
3sin2 30° + 2tan2 60° - 5cos2 45°
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
Prove that:
cosec2 45° - cot2 45° = 1
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Without using tables, evaluate the following: sin230° sin245° + sin260° sin290°.
Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°
If A = 30° and B = 60°, verify that: `(sin("A" + "B"))/(cos"A" . cos"B")` = tanA + tanB
If sin(A +B) = 1(A -B) = 1, find A and B.
If sin(A - B) = `(1)/(2)` and cos(A + B) = `(1)/(2)`, find A and B.
Verify the following equalities:
1 + tan2 30° = sec2 30°
Find the value of the following:
`(tan45^circ)/("cosec"30^circ) + (sec60^circ)/(cot45^circ) - (5sin90^circ)/(2cos0^circ)`
If sin(A + B) = 1 and cos(A – B)= `sqrt(3)/2`, 0° < A + B ≤ 90° and A > B, then find the measures of angles A and B.
If sin α = `1/2`, then find the value of (3 cos α – 4 cos3 α).
`(2/3 sin 0^circ - 4/5 cos 0^circ)` is equal to ______.
Evaluate: sin2 60° + 2tan 45° – cos2 30°.
