Express as the sum or difference of two trigonometric ratios
sin(theta + 75)sin(theta + 15)
@ganeshie8

Question

Express as the sum or difference of two trigonometric ratios
sin(theta + 75)sin(theta + 15)
@ganeshie8

eric_d · Answer

@ikram002p

ganeshie8 · Answer

Lookup 2sinAsinB formula

ikram002p · Answer

lol
i dint get it yet

eric_d · Answer

@ganeshie8

ganeshie8 · Answer

ganeshie8 · Answer

$$\large 2 \sin A \sin B =   \cos(A-B) - \cos (A+B)$$

ganeshie8 · Answer

$$\large  \sin(\theta + 75)\sin(\theta + 15) = \dfrac{1}{2}*2 \sin(\theta + 75)\sin(\theta + 15)   \ \ \\large  = ? $$

ganeshie8 · Answer

Notice that
$A = \theta + 75$
$B = \theta + 15$

ganeshie8 · Answer

$$\large \dfrac{1}{2}*2 \sin(\theta + 75)\sin(\theta + 15)    = ? $$

ganeshie8 · Answer

$A - B =  60$

$A + B = 2\theta + 90$

ganeshie8 · Answer

$$\large \dfrac{1}{2}*2 \sin(\theta + 75)\sin(\theta + 15)    = \dfrac{1}{2}\left[\cos (60)  - \cos (2\theta + 90)\right] $$

ganeshie8 · Answer

see if that looks okay so far

eric_d · Answer

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