For the following questions answer them individually
If $$a = 25, b = 15, c = -10$$, then the value of $$\frac{a^3 + b^3 + c^3 - 3 abc}{(a-b)^2 + (b-c)^2 + (c-a)^2}$$ is
A, B, C are three points on a circle. The tangent at A meets BC produced at T, $$BTA = 40^\circ, CAT = 44^\circ$$. The angle subtended by BC at the centre of the circle
If the length of a chord of a circle at a distance of 12 cm from the centre is 10 cm, then the diameter of the circle is
In ABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR= 2 cm. then BC =
If $$\sin^2 \alpha + \sin^2 \beta$$ , then the value of $$\cos \frac{\alpha + \beta}{2}$$ is
The value of $$\cot \frac{\pi}{20}Â \cot \frac{3\pi}{20}\cot \frac{5\pi}{20}\cot \frac{7\pi}{20}\cot \frac{9\pi}{20}$$ is
If $$\sin \theta + \cos \theta = \frac{17}{13} , 0 < \theta < 90^\circ$$ ,then the value of $$\sin \theta - \cos \theta$$ is
If $$\tan \theta .\tan 2\theta = 1$$, then the value of $$\sin^2 2\theta + \tan^2 2\theta$$ is equal to
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