11th Std Math Practical
Mathematics and Statistics (Arts and Science)
Answers (Solutions)
Practical No.3
2) Trigonometry-2
Practical Session No. 3-Trigonometry-2
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- Apparatus
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- Observations/Table
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- Short Answer Questions :
Practical Session No. 3Trigonometry -2
(1) Show that (cos𝜃𝜃+𝑖 sin𝜃𝜃)3=cos3𝜃𝜃+𝑖 sin3𝜃𝜃
(2) Show that cos3𝜃𝜃−sin3𝜃𝜃 =(cos𝜃𝜃+sin𝜃𝜃)(1−2sin2𝜃𝜃)
(3) Prove that cos2𝜃𝜃+cos2(𝜃𝜃+1200)+cos2(𝜃𝜃−1200)=32
(4) If 𝐴𝐴+𝐵 +𝐶𝐶=𝜋𝜋 then prove thatcos2𝐴𝐴+cos2𝐵 +cos2𝐶𝐶=1−2cos𝐴𝐴cos𝐵 cos𝐶𝐶.Hence prove that cos600=12.
(5) Find the values of sin180 and cos180.
(6) If tan𝐴𝐴=56 and tan𝐵 =111 then show that 𝐴𝐴+𝐵 =𝜋𝜋4 𝑜𝑜𝑜𝑜5𝜋𝜋4.
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Practical Session No. 3
Trigonometry -2
(1) Show that (cos𝜃𝜃+𝑖 sin𝜃𝜃)3=cos3𝜃𝜃+𝑖 sin3𝜃𝜃
(2) Show that cos3𝜃𝜃−sin3𝜃𝜃 =(cos𝜃𝜃+sin𝜃𝜃)(1−2sin2𝜃𝜃)
(3) Prove that cos2𝜃𝜃+cos2(𝜃𝜃+1200)+cos2(𝜃𝜃−1200)=32
(4) If 𝐴𝐴+𝐵 +𝐶𝐶=𝜋𝜋 then prove that
cos2𝐴𝐴+cos2𝐵 +cos2𝐶𝐶=1−2cos𝐴𝐴cos𝐵 cos𝐶𝐶.
Hence prove that cos600=12.
(5) Find the values of sin180 and cos180.
(6) If tan𝐴𝐴=56 and tan𝐵 =111 then show that 𝐴𝐴+𝐵 =𝜋𝜋4 𝑜𝑜𝑜𝑜5𝜋𝜋4.
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