Home
Class 10
MATHS
(cos 70^@)/(sin 20^@) + (cos 59^@)/(sin ...

` (cos 70^@)/(sin 20^@) + (cos 59^@)/(sin 31^@) = 8 sin^2 30^@`

Text Solution

Verified by Experts

Here, we will use `sin(90-theta) = costheta and cos(90-theta) = sintheta`
` L.H.S. = (cos70^@/sin20^@) + (cos59^@/sin31^@)`
`= (cos(90-20)^@/sin20^@) + (cos(90-31)^@/sin31^@)`
`= (sin20^@/sin20^@) + (sin31^@/sin31^@)`
`=1+1 = 2`
`R.H.S. = 8sin^2 30^@ = 8(1/2)^2 = 2`
`:. L.H.S = R.H.S.`
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate : (cos 70^(@))/(sin 20^(@))+(cos 59^(@))/(sin31^(@))-8sin^(2)30^(@)

Evaluate : (cos 70^(@))/(sin 20^(@))+(cos 59^(@))/(sin31^(@))-8sin^(2)30^(@)

Prove that: (i) sin35 sin55-cos35 cos55=0 (ii) (cos70)/(sin20)+(cos59)/(sin31)-8sin^2 30=0

Prove that ((cos70^(@))/(sin20^(@)))+((cos59^(@))/(sin31^(@)))-8cos^(2)60^(@)=0

(cos80^(@))/(sin10^(@))+cos59^(@)cos ec31^(@)=2

(sin 30^@)/(1+cos30^@)+ (1+cos30^@)/(sin 30^@) = ?

Prove that : (i) (sin 70^@)/(cos 20^@)+(cosec 20^@)/(sec 70^@)-2cos 70^@cosec 20^@=0 (ii) (cos 80^@)/(sin 10^@)+cos 59^@cosec 31^@=2 (iii) (2 sin 68^@)/(cos 22^@)-(2 cot 15^@)/(5 tan 75^@)-(3tan 45^@tan 20^@tan 40^@tan 50^@tan 70^@)/(5)=1 (iv) (sin 18^@)/(cos 72^@)+sqrt(3) (tan 10^@ tan 30^@tan 40^@tan 50^@tan 80^@)=2 (v) (7cos 55^@)/(3 sin 35^@)-(4(cos 70^@cosec 20^@))/(3(tan 5^@tan 25^@tan 45^@tan 65^@tan 856^@))=1

Prove that: (i) sin35o sin55o-cos35o cos55o=0 (ii) (cos70o)/(sin200)+(cos590)/(sin31o)-8sin^(2)30o=0

(sin 70^(@) + cos 40^(@))/(cos 70^(@) + sin 40^(@))=