Akvira

  Trigonometric Functions                3.  4. 5. 6.  Example 2: Prove that cos x 1 + sin x = tan ( 4 - x 2 ) . Solution: LHS = cos x 1 + sin x = sin ( 2 - x) 1 + cos ( 2 - x) = 2 sin ( 4 - x 2 ) cos ( 4 - x 2 ) 2 cos 2 ( 4 - x 2 ) = tan ( 4 - x 2 )   = RHS Example 3: Show that 2+ 2+ 2+2 cos 8   = 2 cos Solution: LHS = 2+ 2+ 2+2 cos 8                          = 2+ 2+ 2+2 (1+ cos 8 )     = 2+ 2+ (2cos 4 )               (∵ cos 2𝜃 = 2 cos 2 -1 )                   = 2+ 4 cos 2 2                         (∵ cos 2𝜃 = 2 cos 2 -1 )         ...

Well Defined Collection: Find the odd one out Rabbit, Deer, Tiger , Giraffe, Elephant. 2, 3, 17, 19, 9 , 23 a, e, i, d , o, u 1, 2, 3, 4, 6, 8, 15 , 24 Ganga, Yamuna, Nile , Narmada, Kaveri In the above examples, the odd ones out have been highlighted. As you may observe that other than the highlighted objects, the rest of the objects share some similarities and can thus be grouped together. For instance, Except ‘Tiger’ all other animals are herbivores. Except ‘9’ all other numbers are prime numbers. Except ‘d’ all other alphabets are English vowels. Except ‘15’ all other numbers are factors of 24. Except ‘Nile’ the rest are rivers of India. Each of the above examples is a well-defined collection of objects in the sense that we can definitely decide whether a given particular object belongs to a given collection or not. Again, the collection of five most renowned mathematicians of the world is not well-defined, because the criterion for determining a mathematician as most renowned may ...