Consider the following : 1. { 75^{}}{ 15^{}} + { 12^{}}{ 78^{}} - { 18^{}}{ 72^{}} = 1 2. { 35^{}}{ 55^{}} - { 11^{}}{ 79^{}} + 28^{} \; 62^{} = 1 3. { 18^{}}{ 18^{}} - 59^{} \; 31^{} = 0 Which of the above are correct ?

CDS 2016 PYQ with Answer — Consider the following : 1. { 75^{}}{ 15^{}} + { 12^{}}{ 78^{}} - { 1…

2016 · Q83

Consider the following :

1{ 75^{}}{ 15^{}} + { 12^{}}{ 78^{}} - { 18^{}}{ 72^{}} = 1
2{ 35^{}}{ 55^{}} - { 11^{}}{ 79^{}} + 28^{} \; 62^{} = 1
3{ 18^{}}{ 18^{}} - 59^{} \; 31^{} = 0

Which of the above are correct ?

Elementary MathematicsTrigonometry

A1 and 2 only
B2 and 3 only
C1 and 3 only
D1, 2 and 3

Explanation

The function names are garbled but the angle pairs are complementary, giving the standard forms: (1) tan75°/cot15°+cot12°/tan78°−cot18°/tan72° = 1+1−1 = 1 ✓; (2) tan35°/cot55°−cot11°/tan79°+sin28°sec62° = 1−1+1 = 1 ✓; (3) tan18°cot18°−cos59°sec31° = 1−1 = 0 ✓. All three statements are correct (option D).