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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