Get Started with ixamBee
Start learning 50% faster. Sign in now
sinx + cosx = √2sinx Squaring the equation on both sides, we get. ⇒ sin²x + cos2 x +2sinxcosx = 2sin2 x ⇒ 1 + 2sinx.cosx = 2sin2 x ---- (i) Let sinx - cosx = k ---- (ii) Squaring the equation on both sides, we get. ⇒ 1 - 2sinxcosx = k2 Adding (i) and (ii), we get 2sin2 x + k² = 2 k² = 2(1-sin²x) k² = 2cos2 x k = ± √ (2cos2 x) The value of (sinx – cosx) = ± 2√cosx Alternate- Concept- if (sinx – cosx) =k then (sinx – cosx) =± √(2-k2) Now – k=√2 sin x k2=2sin2x (sinx – cosx) =± √(2-k2) = ± √(2-2sin2x) =± √2 (1-sin2x) = ± √2 cosx.
Atul has Rs.250 with him. He invested 30% of the amount at 4% p.a. for 6 years and rest at 20% p.a. for 5 years. Find the sum of simple interests receiv...
Compound interest received after 2 years on ₹7000 at R% rate of interest compounded annually is ₹1164.8. Find the value of R.
What sum will give Rs. 279 as the difference between simple interest and compound interest at 20% in 1year 6 months compounded half yearly?
A person invested Rs. 75,000 at an annual compound interest rate of 12%, compounded annually for 12 months. How much more profit would he have earned if...
A sum of money, invested for 6 years on 5% per annum simple interest, amounted to ₹169 on maturity. What was the sun invested?
The difference between the compound interest, compounded annually and simple interest on Rs. ‘P’ at the rate of 25% p.a. for 2 years, is Rs. 150. If...
A sum, when invested at 12(½)% simple interest per annum, amounts to ₹8,250 after 2 years. What is the simple interest?
Suresh earned an interest of Rs. 516 on principal amount of Rs. 1600 at some rate of compound interest in 2 years. How much more/less interest would he ...
The difference between the compound interest compounded annually and simple interest of a sum at 6% p.a. for 2 years is Rs. 36. Find the sum.
Rs.5400 is divided into two parts such that if one part be invested at 6% and the other at 9%, the annual interest from both the investments is Rs. 435....
