<prompt> Ikiwa sqrt2 sin 10circ inaweza kuandikwa kama cos theta - sintheta kwa pembe kali theta, theta ni nini? Toa jibu lako kwa digrii, si radians.  <response>: Tuna sintheta cos90circ - theta, hivyocos theta - sintheta costheta -cos90circ-theta.Kutumia tofauti ya fomula ya kosine inatoaanzaaligncos theta - cos90circ - theta 2sinfractheta 90circ - theta2sinfrac90circ -theta - theta2 2sin45circsinfrac90circ - 2theta2 sqrt2sinfrac90circ - 2theta2.endalignTuna sqrt2sin10circ sqrt2sinfrac90circ - 2theta2 wakati 10circ frac90circ - 2theta2. Kwa hiyo, 90circ - 2theta 20circ, na theta 35circ.Ingawa sin 10circ sin 170circ sin -190circ nk., kwa sababu theta ni ya papo hapo, -45circ frac90 circ - 2theta2 45circ na kwa hivyo hakuna uwezekano wowote kati ya hizi husababisha theta kali. 