Question

cos 48 - sin 12 =√5+1/8

Answer 1

i think it should be cos^2 48 - sin^2 12...
Cos²48° - sin²12° 
we know , 
sin(90 - ∅) = cos∅
so, 
sin12° = sin(90-78) = cos78°

cos²48° - cos²78°

[use, a² - b² = (a - b)(a + b) ] 

= (cos48° + cos78°)(cos48°-cos78°)

[ use, formula , 
cosC +cosD = 2cos(C+ D)/2.cos(C-D)/2 
cosC - cosD = 2sin(C +D)/2 .sin(D - C)/2 ]

= 2cos63°.cos15°.2sin63°.sin15°

[use, 2sinA.cosA = sin2A ] 

=sin30.sin126°

= 1/2 sin(90+36°)

=1/2. cos36°

put cos36° = 1/4(√5 +1)

= 1/2 × 1/4 (√5 + 1) 

= (√5 + 1)/8