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ICSE Class X Mid-term 2020 : Mathematics

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Ruby Peter
Bishop Cotton Girls' School (BCGS), Bangalore

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CISCE VIRTUAL LEARNING SERIES LESSON: MATHEMATICS TRIGONOMETRIC IDENTITIES (SESSION 2) October 19th, 2020 Response to Questions posed by students during the live Lesson: S.No. 1. Questions Answers 1 cos A Prove that 1+cos A = sinA 1+cosA . Yes you may. 1 This sum is proved by taking LHS. How will we prove the sum from the RHS? Prove that 1+ = RHS = 1+ 1+ 2 = (1+ )2 1 2 = (1+ )2 (1+ )(1 ) = (1+ )(1+ ) 1 = 1+ LHS 2. Prove that When proving an identity, it is advisable to start 4 2 = 4 + 2 . from one side and prove equal to the other side. Can we prove this identity by transferring a term from LHS to RHS or RHS to LHS? Follow the rule for all sums. 4 2 = 4 + 2 LHS= 2 ( 2 1) = (1 + 2 ) 2 = 2 + 4 = 4 + 2 = RHS Proved S.No. Questions 3. How do Answers we solve a problem like 2 2 = 2 2 2 2 = 2 2 , LHS= 2 2 which involves two different angles and ? = 1 2 (1 2 ) = 1 2 1 + 2 = 2 2 4. As we have algebraic equation, do we have Yes trigonometric equation? Example (i) = = 1 = 45 = 45 Example (i) 2 2 + 1 = 0 ( 1)2 = 0 1 = 0 1 = 0 = 1 = 90 = 90 5. Is it correct to write: cos(A + B) = cosA + cosB No. If we take A=30 and B=60 LHS=cos(A + B) = cos(30 + 60 ) RHS= cosA + cosB = cos 90 =1 = cos30 + cos60 = 3 2 + 1 2 = 3+1 2 Hence ( + ) + S.No. Questions Answers 6. Whenever we use any algebraic identity in the It is better to write them so that you do not go solution, is it important to mention the wrong while applying them. identity which we have used? 7. Is it necessary to learn how to use Yes. It is a part of the ICSE 2021 Scope of Syllabus. trigonometric tables? 8. Its application is there in Heights and Distances. If + sin = and = Here 2 = ( + )2 = 2 + 2 + , prove that 2 2 = 4 2 2 = ( )2 = and 2 + 2 2 2 2 = 4 = 4. = 2 4 and = ( + sin )( ) 2 = 2 2 = 2 2 = 2 2 2 2 = 2 (1 2 ) 2 4 Therefore = 2 = = 4 2 2 2 4 = 4 2 2 = 4 2 = 4 9. Prove: 2 1 2 2 2 = 2 2 1 Hence proved. 2 = 1 2 2 = 2 2 = 2 2 (1 + 2 ) 2 = 2 2 2 2 = 1 + 2 2 2 1 = 10. In 2021 Mathematics syllabus are angles Yes other than standard angles are included? 2 2 S.No. Questions Answers 11. Prove that Yes, in the following way: (Sec A-Cosec A) (1+tan A +cot A) =tan A . Sec 1 1 sin cos = (cos sin ) (1 + cos + sin ) A - cot A. Cosec A . + 2 + 2 Can we prove both sides to a common = ( ) ( answer, and not a direct proof? = . ( )( 2 + + 2 ) 2 . 2 ) = 3 3 2 . 2 = = 1 1 . . 2 = 2 3 3 2 . 2 Hence LHS=RHS 12. Prove that: 1+ + = 1+ + + + = 2( + ) = ( + ) + ( + ) = ( + ) + ( + ) = ( + ) + ( + ) = ( + ) = 13. Can we solve the trigonometric identities Yes, you may but for complex sums this method using right angled triangle and applying the may become complicated. It is more convenient to relation among hypotenuse? perpendicular, base, prove by using other standard identities. S.No. Questions Answers 14. Prove that 1+ = ( )2 1 = 1 1 1 = 1 + 1 + 1 (1 )2 = (1)2 ( )2 = = (1 )2 1 2 (1 )2 =( 2 1 2 1 ) 2 = ( ) = ( )2 = 15. 16. In board examination do we get marks for Marks are given for necessary correct relevant every step? steps. Prove that = 2( 6 + 6 ) 3( 4 + 4 ) +1 2( 6 + 6 ) 3( 4 + 4 ) + 1 = 0 = 2{( 2 )3 + ( 2 )3 } 3{( 2 )2 + ( 2 )2 } + 1 = 2{( 2 + 2 )3 3 2 . 2 ( 2 + 2 )} 3{( 2 + 2 )2 2 2 2 } + 1 = 2(1 3 2 . 2 ) 3(1 2 2 . 2 ) + 1 = 2 6 2 . 2 3 + 6 2 . 2 + 1 = 0 = 17. Is it necessary to write the basic trigonometric The sum will not be marked wrong if you do not identities which we are using, beside the write the standard identities used. sum?

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