Some very important SLC questions

Short questions : Note This is just test; original post is here http://mb9851.wordpress.com/

Q. No .3
(i) If A+B = 45, prove that (1+tanA)(1+tanB)=2

(ii) If A+B = 45, prove that: (cotA-1)(cotB-1) = 2

(iii) If A+B =225, prove that (tanA+1)(tanB+1)=2

(ii) If A+B = 225, prove that: (1-cotA)(1-cotB) = 2

Q. No. 4 Prove that:

  1. (2cosA+1)(2cosA-1)=2cos2A+1
  2. (2sinA-1)(2sinA+1)=1-2cos2A
  3. (2cos{A \over 2}-1)(2cos{A \over 2}+1)=1+2cosA
  4. (2sin{A \over 2} -1)(2sin {A \over 2} +1) = 1-2cosA
  5. (2cos2A+1)(2cos2A-1)=1+2cos4A
  6. (2sin2A -1)(2sin2A+1)=1-2cos4A

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