1.

Find the value of : (i) `sin75^o` (ii) `tan15^o`

Answer» (i) `sin 75^@ = sin(45^@ + 30^@)`
using identity `sin(a+b) = sinacosb + cosasinb`
`= sin45^@cos30^@ + cos45^@sin30^@`
`= 1/sqrt2 * sqrt3/2 + 1/sqrt2 * 1/2 `
`= sqrt3/(2sqrt2) + 1/(2sqrt2)`
`= (sqrt3 + 1)/(2sqrt2)`
(ii) `tan 15^@ = tan(45^@- 30^@)`
using identity `tan(a-b) = (tana- tanb)/(1+tan a tan b)`
`= (tan 45^@ - tan 30^@)/(1 + tan45^@tan30^@)`
`= (1-1/sqrt3)/(1 + 1*1/sqrt3)`
`= ((sqrt3 - 1)/(sqrt3))/((sqrt3 + 1)/sqrt3)`
`= (sqrt3 -1)/(sqrt3+1) * (sqrt3 - 1)/(sqrt3 -1) `
`= (sqrt3 - 1)^@/((sqrt3)^2 - 1^2)`
`= (3+1 - 2sqrt3)/(3-1)`
`= (4-2sqrt3)/2`
`2- sqrt3`
answer


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