Question

3. Given: A and B are positive acute angles, where sin A = { and cos B = 3 Find the exact value of sin(A+B). 4. Given: angles A and B are in Quadrant I, where 5 tan 4= - and sin B=- V74 Find the exact value of tan(A+B). 5. Given: A lies in Quadrant III and B lies in Quadrant II, sin A=-.- and cos B= Find the exact value of cos(A-B). 17

Answer 1

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3. and cost-4 12 Sin A-S OL A, B CI so all trigometric function will be the. S02 COSA = di-sina VI-(5/32 = 5 161-25 - H1 SinB = √ i-cos?B = √ 1 - MLs)2 = /25-16 = 9 sin (A + B ) = SinA COSB + COSA . SinB = 5/137 4 2 + 1 2 3 x 3 = 20 5 + 31 7 tand = and sinB = 5/74 A,B are in Ist quad! tan B = sinB - 5/74 51474 ✓ 1-SinB 5/114 - 1572) 11-25 STIG - 5 tan (A + B) = = 117 +517 tant + tanB rant tanB t

& 5 quad. I sin the 17 SinA = -8 and cos B = -4 A quad. Il cos B COSA=-11-sinta = -√ 1-(8/2)2 = -√289.64 - 225 - COSA LA 289-64 289 (225 ▼ 289 sinB = + J 1- Cosh - |- (-4/5)2 = /25-16 - 1 2 3 4 so COSCA-B) = Cost CosB + sinA.sinB () + (x2) 17 - 03 12 24 85 TZ 36 85