This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Huu ni mfumo wa kutatua swali la hisabati. Step 1: Rahisisha mlinganyo uliotolewa. Mlinganyo uliotolewa ni: (30^ - 45^) = ( + 15^) Rahisisha upande wa kushoto: (-15^) = ( + 15^) Step 2: Tumia kanuni za trigonometria kuunganisha sine na cosine. Tunajua kwamba x = (90^ - x). Hivyo, (-15^) inaweza kuandikwa kama: (-15^) = (90^ - (-15^)) = (90^ + 15^) = (105^) Sasa mlinganyo unakuwa: (105^) = ( + 15^) Step 3: Tatua kwa . Ikiwa A = B, basi A = ± B + 360^ n, ambapo n ni nambari kamili. Hivyo, tuna visa viwili: Kesi ya 1: 105^ = + 15^ + 360^ n Chukua n=0 kwa suluhisho rahisi: 105^ = + 15^ = 105^ - 15^ = 90^ Ikiwa = 90^, basi = (90^), ambayo haijafafanuliwa. Kwa kawaida, hii si jibu linalotarajiwa kwa swali la "tafuta ". Kesi ya 2: 105^ = -( + 15^) + 360^ n Chukua n=0 kwa suluhisho rahisi: 105^ = - - 15^ = -15^ - 105^ = -120^ Step 4: Kokotoa kwa thamani halali ya . Tunatumia = -120^. (-120^) Tunajua kwamba (-x) = - x. Hivyo, (-120^) = - (120^). Pia, (120^) = (180^ - 60^). Kwa kuwa 120^ iko katika roboduara ya pili, ni hasi. (180^ - 60^) = - (60^). Tunajua (60^) = sqrt(3). Hivyo, (120^) = -sqrt(3). Kwa hiyo, (-120^) = -(-sqrt(3)) = sqrt(3). Jibu la mwisho ni sqrt(3). Tuma swali linalofuata 📸