Step-by-step explanation:
note that
sin²x = (1-cos²x)
LHS= cos²x - 2 sin²x
= cos²x - 2(1-cos²x)
= cos²x - 2 + 2cos²x
= 3cos²x - 2
or
cos²x = (1-sin²x)
LHS= cos²x - 2 sin²x
=1-sin²x - 2 sin²x
= 1-3sin²x
Answer:
1) By SAS theorem, ΔADE≅ΔCDF
2) By SSS theorem, ΔBDE≅ΔBDF
Step-by-step explanation:
Consider isosceles triangle ABC (see diagram).
1. In triangles ADE and CDF:
- AD≅DC (since BD is median, then it divides side AC in two congruent parts);
- AE≅CF (given);
- ∠A≅∠C (triangle ABC is isosceles, then angles adjacent to the base are congruent).
By SAS theorem, ΔADE≅ΔCDF.
2. In triangles BDE and BDF:
- side BD is common;
- DE≅DF (ΔADE≅ΔCDF, then congruent triangles have congruent corresponding sides);
- BE≅FB (triangle ABC is isosceles, AB≅BC, AE≅CF, then BE=AB-AE, FB=BC-CF).
Be SSS theorem, ΔBDE≅ΔBDF.
Answer: rhombus
Step-by-step explanation: because trump is the best president