1. If secA+tanA=p, then show that secA-tnaA=1/p
2. Evaluate:
(i) sec²60°+sec0°
(ii) sin12°+sin78°
3. Simply:
(i) (1-sinA)(tanA+secA)
(ii)(secA+cosA)(cotA+tanA)
4. If a sweet shopkeeper prepares 396 gulab jamun and 342 ras-gullas. He packs them in containers. Each container consist of either gulab jamuns or ras-gullas in equal number pieces. Find the number of pieces he should put in each box so that number boxes are least.
5. If a polynomial x⁴+5x³+4x²-10x-12 has two zeroes -2 and -3, then find the other zeroes
6. ∆ABC is right angled at B. P and Q are the mid points of AB and BC, then prove that:
(i)4PC²=4BC²+AB²
(ii)4AQ²=4AB²+BC²
(iii)5AC²=4PC²+4AQ²
7. In rhombus ABCD, prove that AB²+BC²+CD²+AC²=AC²+BD².
8. Divide y⁴+y²+1 by y³+y and verify the division lemma.
9. BL and CM are the medians of ∆ABC right angled at A. Prove that 4(BL²+CM²)=5BC².
10. If secB+tanB=p then show that sinB=(p²-1)/(p²+1).
11. Given HCF(306, 657)=9, find LCM(306, 657).
