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in any triangle abc prove
a cosA+b cosB+c cosC=2a sin B sin C
1.if cos(A+B) sin(C+D)=cos(A-B) sin(C-D), show that cotA cotB cotC = cotD
Show that the equation cosec x=4ab/(a+ b)2 ,(ab>0) is possible if a=b
if cos(a+b) = 0 then find the value of sin(5a+6b)
If 2 tanα = 3 tanβ , prove that tan (α-β) = sin 2β / 5 - cos 2β.
In a triangle ABC , if angle C is obtuse, then the range of tanAtanB is ?
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Syllabus
in any triangle abc prove
a cosA+b cosB+c cosC=2a sin B sin C
1.if cos(A+B) sin(C+D)=cos(A-B) sin(C-D), show that cotA cotB cotC = cotD
rnShow that the equation cosec x=4ab/(a+ b)2 ,(ab>0) is possible if a=b
49. Determine maximum value of ( 5sinx - 12cosx ) ( 5cosx + 12sinx ).
if cos(a+b) = 0 then find the value of sin(5a+6b)
If 2 tanα = 3 tanβ , prove that tan (α-β) = sin 2β / 5 - cos 2β.
In a triangle ABC , if angle C is obtuse, then the range of tanAtanB is ?
4tan^2x - 2sec^2x +1 =0 ,x belongs to [0,20]
prove that:
i) tan(A+B)=2tanA
ii) 2sin B= cos A sin(A+B)
iii)sin B= sin A cos(A+B)
iv) [cot A + cot(A+B)] [cot B -3 cot(2A+B)] =6
39. In the formula , find within what limits must lie when
i) The two positive signs are taken
ii) The two negative signs are takes
iii) First sign negative and seconds sign positive.
Sin A + cos A=??
cot 7 π /16 + 2cot 3 π /8 + cot 15 π /16
(1) 1 (2) 2 (3) (4)
60. The value of tan9 - tan27 - tan63 + tan81 is
(1) 6
(2) 4
(3) 10
(4) 20
(1) (2) (3) (4)