Solve this: Use the following information to answer the next question. cos p - q × sin r - s = cos p + q × sin r + s a n d c o t s = x , c o t r = y , a n d c o t q = z W h a t i s t h e v a l u e o f c o t p ? A . x y z B . x y + z C . x y z D . x y z Share with your friends Share 0 Sandeep Saurav answered this Dear Student, Given : cot s=x, cot r=y and cot q=zand cos (p-q)×sin (r-s)=cos (p+q)×sin (r+s)To Calculate : Value of cot pSolution : using the formulaecos (A-B)=cos A cos B+sin A sin Bcos (A+B)=cos A cos B-sin A sin Bsin (A-B)=sin A cos B+cos A sin Bsin (A-B)=sin A cos B-cos A sin B⇒cos (p-q)×sin (r-s)=cos (p+q)×sin (r+s)⇒(cos p cos q+sin p sin q)(sin r cos s-cos r sin s)=(cos p cos q-sin p sin q)(sin r cos s+cos r sin s)⇒cos p cos q sin r cos s-cos p cos q cos r sin s+sin p sin q sin r cos s-sin p sin q cos r sin s=cos p cos q sin r cos s+cos p cos q cos r sin s-sin p sin q sin r cos s-sin p sin q cos r sin s ⇒-cos p cos q cos r sin s+sin p sin q sin r cos s=cos p cos q cos r sin s-sin p sin q sin r cos s ⇒2 cos p cos q cos r sin s=2 sin p sin q sin r cos s⇒cos p cos q cos r sin ssin p sin q sin r cos s=1⇒cos psin p× cos qsin q× cos rsin rcos ssin s=1⇒cot p× cot q× cot rcot s=1⇒cot p=cot scot q×cot r⇒cot p=xzyHence, cot p=xyz. Hope this information will clear your doubts about topic. If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible. Keep posting!! Regards 0 View Full Answer
