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Statement I : If sin alpha = 12/13, (0 &...

Statement I : If `sin alpha = 12/13, (0 < alpha < pi/2)` and `cos beta = -3/5, (pi < beta < (3pi)/2)` then `sin(alpha + beta) = 56/65`. Statement II : If `theta and phi` are angles in the first quadrant such that `tan theta = 1/7 and sin phi = 1/sqrt10` then `theta + 2phi = 45^@` (i) only I (ii) only II (iii) Both I and II (iv) Neither I nor II

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Statement I: If sin alpha = 12/13, (0 lt alpha lt pi/2) and cos beta =-3/5,(pi lt beta lt (3pi)/2) , then sin(alpha + beta) = 56/65 Statement II : If theta and phi , are angles in the first quadrant such that tan theta =1/7 and sin phi =1/sqrt(10) , then theta + 2phi = 45^(@) Which of the above statements is correct?

sin alpha=(12)/(13) (0 lt alpha lt (pi)/(2)r) cos beta=-(3)/(5)(pi lt beta lt (3 pi)/(2)) then sin (alpha+beta) is

If sin theta =12/13 (0 lt theta lt (pi)/(2)) and cos phi =-3/5 (pi lt phi lt (3pi)/(2)) then the value of sin (theta+ phi) will be-

If sin theta = (12)/(13) (0 lt theta lt (pi)/(2)) and cos phi = (-3)/(5) (pi lt phi lt (3pi)/(2)) then 65 sin (theta + phi) + 60 equals to "_______"

If 13 sin alpha = 12, where pi//2 lt alpha lt pi, and 3 sec beta = 5, where 3pi//2 lt beta lt 2pi , evaluate : 5tan alpha+3 tan^(2)beta.

If theta and phi lie in the first quadrant such that sin theta =(8)/(17) "and cos " phi =(12)/(13) find the values of (i) " sin"(theta- phi) " "(ii) " cos " (theta + phi) " " (iii) " tan " (theta - phi)

If sin alpha = 3/5, tan beta = 1/2 and pi/2 lt alpha lt pi lt beta lt (3pi)/2 , show that 8 tan alpha - sqrt(5) sec beta = - 7/2 .

cos (alpha+beta)=(3)/(5) and sin (alpha-beta)=(3)/(5) and 0 lt alpha, beta lt (pi)/(2) then sin 2 alpha=