If 0 degree<A, B < 90°, such that cos A =5/13 and sin B = 4/5 find the value of sin (A - B)
Answers
Answered by
25
Step-by-step explanation:
cosA=5/13
∴, sinA
=√(1-cos²A)
=√(1-25/169)
=√(169-25)/169
=√(144/169)
=12/13 [neglecting the negative sign since A is an acute angle]
sinB=4/5
∴. cosB
=√(1-sin²B)
=√(1-16/25)
=√(25-16)/25
=√(9/25)
=3/5 [neglecting the negative sign since A is an acute angle]
∴, sin(A+B)
=sinAcosB+cosAsinB
=12/13×3/5+5/13×4/5
=36/65+20/65
=(36+20)/65
=56/65
Answered by
4
Answer:
sin (A+B) =56/65
Step-by-step explanation:
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