-Y
tan (AB
tan (A+B) =
2
find tan 2A
tan 2 B
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11th
Maths
Trigonometric Functions
Trigonometric Functions of Sum and Difference of Two angles
If x = tan (A + B) + tan (A...
MATHS
If x=tan(A+B)+tan(A−B),y=tan(A+B)tan(A−B) then
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ANSWER
x=tan(A+B)+tan(A−B)
=
1−tanAtanB
tanA+tanB
+
1+tanAtanB
tanA−tanB
=
1−
cosA
sinA
cosB
sinB
cosA
sinA
+
cosB
sinB
+
1+
cosA
sinA
cosB
sinB
cosA
sinA
−
cosB
sinB
=
cos(A+B)
sin(A+B)
+
cos(A−B)
sin(A−B)
=
cos(A+B)cos(A−B)
sin(A+B)cos(A−B)+sin(A−B)cos(A+B)
=
cos2A+cos2B
sin2A
And
y=tan(A+B)×tan(A−B)
=
1−tanAtanB
tanA+tanB
×
1+tanAtanB
tanA−tanB
=
1−
cosA
sinA
cosB
sinB
cosA
sinA
+
cosB
sinB
×
1+
cosA
sinA
cosB
sinB
cosA
sinA
−
cosB
sinB
=
cos(A+B)
sin(A+B)
×
cos(A−B)
sin(A−B)
=
cos2B+cos2A
cos2B−cos2A