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If-sin-P-8-17-where-3pi-2-lt-P-lt-2pi-and-cos-Q-24-25-where-pi-lt-Q-lt-3pi-2-what-is-the-value-of-cos-2P-Q-




Question Number 116448 by bobhans last updated on 04/Oct/20
If sin (P) = −(8/(17)) ,where ((3π)/2)<P<2π  and cos (Q)=−((24)/(25)), where π<Q<((3π)/2)  what is the value of cos (2P+Q) =?
Ifsin(P)=817,where3π2<P<2πandcos(Q)=2425,whereπ<Q<3π2whatisthevalueofcos(2P+Q)=?
Answered by bemath last updated on 04/Oct/20
(1) cos (P)= ((15)/(17)) ; sin (Q)=−(7/(25))  ⇒cos (2P+Q) = cos (2P).cos (Q)−sin (2P).sin (Q)                                 =−((24)/(25))(1−2(((64)/(289))))−{2(−(8/(17)))(((15)/(17)))}.(−(7/(25)))               = −((24)/(25))(((161)/(289)))−(((240)/(289))).((7/(25)))               = −((5544)/(289×25)) = −((5544)/(7225))
(1)cos(P)=1517;sin(Q)=725cos(2P+Q)=cos(2P).cos(Q)sin(2P).sin(Q)=2425(12(64289)){2(817)(1517)}.(725)=2425(161289)(240289).(725)=5544289×25=55447225
Answered by mr W last updated on 04/Oct/20
sin P=−(8/(17))  ⇒cos P=((√(17^2 −8^2 ))/(17))=((15)/(17))  cos Q=−((24)/(25))  ⇒sin Q=−((√(25^2 −24^2 ))/(25))=−(7/(25))  cos (2P+Q)=cos 2P cos Q−sin 2P sin Q  =(2 cos^2  P−1) cos Q−2 sin P cos P sin Q  =(2×((15^2 )/(17^2 ))−1)(−((24)/(25)))−2(−(8/(17))×((15)/(17)))(−(7/(25)))  =−(((2×15^2 −17^2 )×24+2×8×15×7)/(17^2 ×25))  =−((5544)/(7225))
sinP=817cosP=1728217=1517cosQ=2425sinQ=25224225=725cos(2P+Q)=cos2PcosQsin2PsinQ=(2cos2P1)cosQ2sinPcosPsinQ=(2×1521721)(2425)2(817×1517)(725)=(2×152172)×24+2×8×15×7172×25=55447225
Commented by I want to learn more last updated on 04/Oct/20
Sweet sir
Sweetsir
Commented by I want to learn more last updated on 04/Oct/20
Commented by I want to learn more last updated on 04/Oct/20
Sir please tag this your solution. I can only see the image. but i think it is  your solution sir
Sirpleasetagthisyoursolution.Icanonlyseetheimage.butithinkitisyoursolutionsir
Commented by mr W last updated on 04/Oct/20
what is the question?
whatisthequestion?
Commented by I want to learn more last updated on 04/Oct/20
I only see the image saved sir, no question number, am only thinking it  could be find the radius of the small circle. with the lines you drew on the  diagram
Ionlyseetheimagesavedsir,noquestionnumber,amonlythinkingitcouldbefindtheradiusofthesmallcircle.withthelinesyoudrewonthediagram
Commented by mr W last updated on 04/Oct/20
see Q116466
seeQ116466
Commented by I want to learn more last updated on 04/Oct/20
Am really grateful sir
Amreallygratefulsir

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