Please prove no. 4,6,8 and 10. 3 points for each answer. Class 10 ICSE Maths.
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4. tan A-cot A= (sin A/cos A) - (cos A/sin A)
=(sin^2 A - cos^2 A)/ sinA.cosA
=(1-cos^2 A- cos^2 A)/ SinA.cosA
=(1-2cos^2 A)/ sin A. cos A
proved
6. (1-tanA)^2 + (1+tan A)^2
=1+tan^2A-2tanA+1+tan^2A+2tanA
=2+2tan^2A
=2(1+tan^2A)
=2sec^2A
10. sec^2A+cosec^2A
=(1/cos^2A)+(1/sin^2A)
=(sin^2A+cos^2A)/cos^2A.sin^2A
=1/cos^2A.sin^2A
=sec^2A.cosec^A...............proved
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