Q55.If x = ∑∞n=0 (−1)ntan2θ and y = ∑∞n=0 cos2nθ, for 0 < θ < π4 , then: (1) x(1 + y) = 1 (2) y(1 −x) = 1 (3) y(1 + x) = 1 (4) x(1 −y) = 1 x when π
What This Question Tests
This question involves evaluating two infinite geometric series using trigonometric identities to simplify expressions and find a relationship between the sums.
Concepts Tested
Formulas Used
S_infinity = a / (1 - r) (for |r| < 1)
tan^2θ + 1 = sec^2θ
1/sec^2θ = cos^2θ
📚 NCERT Sections This Tests
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Geometric Series (Infinite)
- Year
- 2020
- Shift
- 09 Jan Shift 2
- Q Number
- Q55
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series; Class 11 Mathematics Ch 3: Trigonometric Functions
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